Glasses and glass ceramics including a metal oxide concentration gradient

ABSTRACT

Embodiments of a glass-based article including a first surface and a second surface opposing the first surface defining a thickness (t) of about 3 millimeters or less (e.g., about 1 millimeter or less), and a stress profile, wherein all points of the stress profile between a thickness range from about 0·t up to 0.3·t and from greater than 0.7·t, comprise a tangent that is less than about −0.1 MPa/micrometers or greater than about 0.1 MPa/micrometers, are disclosed. In some embodiments, the glass-based article includes a non-zero metal oxide concentration that varies along at least a portion of the thickness (e.g., 0·t to about 0.3·t). In some embodiments, the concentration of metal oxide or alkali metal oxide decreases from the first surface to a point between the first surface and the second surface and increases from the point to the second surface. The concentration of the metal oxide may be about 0.05 mol % or greater or about 0.5 mol % or greater throughout the thickness. Methods for forming such glass-based articles are also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application and claims the benefit ofpriority under 35 U.S.C. § 120 of U.S. application Ser. No. 14/878,429,filed on Oct. 8, 2015, which in turn, claims the benefit of priorityunder 35 U.S.C. § 119 of U.S. Provisional Application Ser. No.62/194,967, filed on Jul. 21, 2015, U.S. Provisional Application Ser.No. 62/171,110, filed on Jun. 4, 2015, U.S. Provisional Application Ser.No. 62/117,585, filed on Feb. 18, 2015, and U.S. Provisional ApplicationSer. No. 62/061,372, filed on Oct. 8, 2014, the contents of each ofwhich are relied upon and incorporated herein by reference in theirentireties.

BACKGROUND

The disclosure relates to glass-based articles exhibiting improveddamage resistance, including improved fracture resistance, and moreparticularly to glass and glass ceramic articles exhibiting a non-zerometal oxide concentration gradient or concentration that varies along asubstantial portion of the thickness.

Glass-based articles often experience severe impacts that can introducelarge flaws into a surface of such articles. Such flaws may extend todepths of up to about 200 micrometers from the surface. Traditionally,thermally tempered glass has been used to prevent failures where suchflaws may be introduced to the glass because thermally tempered glassoften exhibits large compressive stress (CS) layers (e.g., approximately21% of the total thickness of the glass), which can prevent flaws frompropagating and thus, failure. An example of a stress profile generatedby thermal tempering is shown in FIG. 1. In FIG. 1, the thermallytreated glass-based article 100 includes a first surface 101, athickness t₁, and a surface CS 110. The glass-based article 100 exhibitsa CS that decreases from the first surface 101 to a depth of layer (DOL)130, as defined herein, at which depth the stress changes fromcompressive to tensile stress and reaches a maximum central tension (CT)120.

Thermal tempering is currently limited to thick glass-based articles(i.e., glass-based articles having a thickness t₁ of about 3 millimetersor greater) because, to achieve the thermal strengthening and thedesired residual stresses, a sufficient thermal gradient must be formedbetween the core of such articles and the surface. Such thick articlesare undesirable or not practical in many applications such as displays(e.g., consumer electronics, including mobile phones, tablets,computers, navigation systems, and the like), architecture (e.g.,windows, shower panels, countertops etc.), transportation (e.g.,automotive, trains, aircraft, sea craft, etc.), appliances, or anyapplication that requires superior fracture resistance but thin andlight-weight articles.

Known chemically strengthened glass-based articles do not exhibit thestress profile of thermally tempered glass-based articles, althoughchemical strengthening is not limited by the thickness of theglass-based article in the same manner as thermally tempering. Anexample of a stress profile generated by chemical strengthening (e.g.,by ion exchange process), is shown in FIG. 2. In FIG. 2, the chemicallystrengthened glass-based article 200 includes a first surface 201, athickness t₂ and a surface CS 210. The glass-based article 200 exhibitsa CS that decreases from the first surface 201 to a DOC 230, as definedherein, at which depth the stress changes from compressive to tensilestress and reaches a maximum CT 220. As shown in FIG. 2, such profilesexhibit a flat CT region or CT region with a constant or near constanttensile stress and, often, a lower maximum CT value, as compared to themaximum central value shown in FIG. 1.

Accordingly, there is a need for thin glass-based articles that exhibitimproved fracture resistance.

SUMMARY

A first aspect of this disclosure pertains to a glass-based articleincluding a first surface and a second surface opposing the firstsurface defining a thickness (t) (e.g., about 3 millimeters or less, 1millimeter or less or about 0.5 millimeters or less), and a stressprofile extending along the thickness. In one or more embodiments,wherein all points of the stress profile between a thickness range fromabout 0·t up to about 0.3·t and greater than 0.7·t comprise a tangentthat is less than about −0.1 MPa/micrometers or greater than about 0.1MPa/micrometers.

In some embodiments, the glass-based article includes a non-zero metaloxide concentration that varies along a substantial portion of thethickness or the entire thickness. The variation in metal oxideconcentration may be referred to herein as a gradient. In someembodiments, the concentration of a metal oxide is non-zero and varies,both along a thickness range from about 0·t to about 0.3·t. In someembodiments, the concentration of the metal oxide is non-zero and variesalong a thickness range from about 0·t to about 0.35·t, from about 0t toabout 0.4·t, from about 0·t to about 0.45·t or from about 0·t to about0.48·t. The metal oxide may be described as generating a stress in theglass-based article. Variation in metal oxide concentration may includea change of about 0.2 mol % along a thickness segment of about 100micrometers. The variation in concentration may be continuous along theabove-referenced thickness ranges. In some embodiments, the variation inconcentration may be continuous along thickness segments in the rangefrom about 10 micrometers to about 30 micrometers.

In some embodiments, the concentration of the metal oxide decreases fromthe first surface to a point between the first surface and the secondsurface and increases from the point to the second surface.

As used herein, the metal oxide comprises strengthening ions or ionsthat generate CS in a glass-based article. In some embodiments, themetal oxide has the largest ionic diameter of all of the total metaloxides in the glass-based substrate. In one or more embodiments, metaloxide(s) may include alkali metal oxide(s), or combinations of differentmetal oxides or alkali metal oxides. Exemplary metal oxides includeAg₂O. Exemplary alkali metal oxides include any one or more of Li₂O,Na₂O, K₂O, Rb₂O, and Cs₂O. The metal oxide(s) may be present in anon-zero concentration of that particular metal oxide(s) that variesalong a substantial portion or the entire thickness of the glass-basedarticle. In some embodiments, the concentration of the metal oxide(s)decreases from the first surface to a point between the first surfaceand the second surface and increases from the point to the secondsurface. The concentration of the metal oxide(s) may be non-zero at thepoint.

The concentration of the metal oxide(s) may be about 0.05 mol % orgreater or about 1 mol % or greater throughout the thickness. Forexample, the concentration of Na₂O may be about 0.05 mol % or greaterthroughout the thickness of the glass-based article but suchconcentration of Na₂O decreases from the first surface to a pointbetween the first surface and the second surface and increases from thepoint to the second surface. In some examples, the total concentrationof the metal oxide(s) along the entire thickness of the glass-basedarticle is in the range from about 1 mol % to about 20 mol %. In someembodiments, the concentration of the metal oxide(s) near the surfacemay be more than 1 times or 1.5 times (e.g. 5 times, 10 times, 15 timesor even 20 times), the concentration of that same metal oxide(s) at adepth in the range from about 0.4·t to about 0.6·t. The concentration ofthe metal oxide(s) may be determined from a baseline amount of thatmetal oxide(s) concentration in the glass-based article prior to beingmodified to exhibit the concentration profile (i.e., gradient orvariation, as described herein).

In one or more embodiments, the glass-based article includes a firstmetal oxide concentration and a second metal oxide concentration, suchthat the first metal oxide concentration is in the range from about 0mol % to about 15 mol % along a first thickness range from about 0t toabout 0.5t, and the second metal oxide concentration is in the rangefrom about 0 mol % to about 10 mol % from a second thickness range fromabout 0 micrometers to about 25 micrometers. The glass-based article mayinclude an optional third metal oxide concentration. The first metaloxide may be Na₂O and the second metal oxide may be K₂O.

In one or more embodiments, the glass-based article includes a surfaceCS of about 150 MPa or greater or about 200 MPa or greater. In one ormore embodiments, the glass-based article may exhibit a surface CS ofgreater than about 300 MPa, greater than about 600 MPa or greater thanabout 700 MPa. The glass-based article may exhibit a chemical depth ofabout 0.4·t or greater.

In some embodiments, the glass-based article may include a CS layerextending from the first surface to a DOC of about 0.1·t or greater. Insome instances, the glass-based article includes a layer of CT, whichincludes the non-zero metal oxide concentration that varies along asubstantial portion of the thickness t. The layer of CT may exhibit amaximum CT such that the ratio of maximum CT to surface CS is in therange from about 0.01 to about 0.5. The maximum CT may be about 25 MPaor greater.

In one or more embodiments, the glass-based article may exhibit afracture resistance such that, when the glass-based article isfractured, the glass-based article fractures into at least 2fragments/inch². In some instances, the glass-based article may fractureinto 3 fragments/inch² or more, 5 fragments/inch² or more, or 10fragments/inch² or more.

In some instances, the glass-based article may exhibit a stored tensileenergy of about greater than 0 J/m² to less than 20 J/m².

The CT region of one or more embodiments of the glass-based article mayexhibit a stress profile defined by the equation:Stress(x)=MaxCT−(((MaxCT·(n+1))/0.5^(n))·|(x/t)−0.5|^(n)),wherein MaxCT is a maximum CT value and provided as a positive value inunits of MPa, x is position along the thickness (t) in micrometers, andn is between 1.5 and 5 (or between 1.8 to about 2).

The glass-based article may include an amorphous structure, acrystalline structure or a combination thereof. The glass-based articlemay be transparent or opaque. In some embodiments, the glass-basedarticle exhibits a substantially white color or a substantially blackcolor. Additionally or alternatively, the glass-based article mayinclude a colorant that provides a specific color.

A second aspect of this disclosure pertains to an amorphous glasssubstrate comprising a composition including, in mol %, SiO₂ in anamount in the range from about 68 to about 75, Al₂O₃ in an amount in therange from about 12 to about 15, B₂O₃ in an amount in the range fromabout 0.5 to about 5, Li₂O in an amount in the range from about 2 toabout 8, Na₂O in an amount in the range from about 0 to about 6, MgO inan amount in the range from about 1 to about 4, ZnO in an amount in therange from about 0 to about 3, and CaO in an amount in the range fromabout 0 to about 5. In some embodiments, the glass substrate exhibitsany one or more of a ratio of Li₂O to R₂O in the range from about 0.5 toabout 1; a difference between a total amount of R₂O to the amount ofAl₂O₃ in the range from about −5 to about 0; a difference between atotal amount of R_(x)O (in mol %) and the amount of Al₂O₃ in the rangefrom about 0 to about 3; and a ratio of the amount of MgO (in mol %) toa total amount of RO (in mol %) in the range from about 0 to about 2.

In one or more embodiments, the glass substrate is ion-exchangeable. Inother embodiments, the glass substrate is strengthened by an ionexchange process.

A third aspect of this disclosure pertains to a method of forming afracture resistant glass-based article as described herein. Embodimentsof the method include providing a glass-based substrate having a firstsurface and a second surface defining a thickness of about 3 millimeteror less, generating a stress profile in the glass-based substratecomprising a CT layer and a CS layer, wherein the CS layer has a surfaceCS, a chemical depth of about 0.4t or greater and a DOC of about 0.1·tor greater, and wherein the CT layer comprises a maximum CT and theratio of maximum CT to surface CS is from about 0.01 to about 0.5.

Additional features and advantages will be set forth in the detaileddescription which follows, and in part will be readily apparent to thoseskilled in the art from that description or recognized by practicing theembodiments as described herein, including the detailed descriptionwhich follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are merely exemplary, and areintended to provide an overview or framework to understanding the natureand character of the claims. The accompanying drawings are included toprovide a further understanding, and are incorporated in and constitutea part of this specification. The drawings illustrate one or moreembodiment(s), and together with the description serve to explainprinciples and operation of the various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view across a thickness of a known thermallytempered glass-based article;

FIG. 2 is a cross-sectional view across a thickness of a knownchemically strengthened glass-based article;

FIG. 3 is a cross-sectional view across a thickness of a chemicallystrengthened glass-based article according to one or more embodiments ofthis disclosure;

FIG. 4 is a is a schematic cross-sectional view of a ring-on-ringapparatus;

FIG. 5 is a graph showing the concentration of Na₂O in known chemicallystrengthened glass-based articles and glass-based articles according toone or more embodiments of this disclosure;

FIG. 6 is a graph showing CT values and DOC values as a function of ionexchange time, according to one or more embodiments of this disclosure;

FIG. 7 is a graph comparing the stress profiles as a function of depthof known chemically strengthened glass-based articles and glass-basedarticles, according to one or more embodiments of this disclosure

FIG. 8 shows a graph of the stress profiles of a known chemicallystrengthened glass and glass-ceramic;

FIG. 9 shows a graph of the stress profiles of a glass and glass-ceramicaccording to one or more embodiments of this disclosure;

FIG. 9A shows a graph of the failure height in drop testing of Example3D;

FIG. 10 is a graph comparing a known stress profile of a chemicallystrengthened glass-based article and a glass-based article according toone or more embodiments of this disclosure;

FIG. 11 is a graph showing the stress profiles of Examples 4A-4D asfunction of thickness;

FIG. 12 is a graph showing discrete stored tensile energy data pointsfor Examples 4B-4D;

FIG. 13 is a graph showing the concentration of K₂O and Na₂O as afunction of depth in Examples 4A-4D;

FIG. 14 is a graph showing the same data as FIG. 12, but with adifferent scale to more clearly illustrate the concentration of Na₂O asa function of depth;

FIG. 15 is a graph showing the stress profiles of Examples 4A and 4C-4Fas a function of depth;

FIG. 16 is a graph showing different scale of FIG. 14;

FIG. 17 is a graph showing the stress profiles of Examples 5A-5G as afunction of depth;

FIG. 18 is a graph showing the DOC values for Examples 5A-5G as afunction of duration of the second and/or third ion exchange steps;

FIG. 19 is a graph showing the CT values Examples 5A-5G as a function ofduration of the second and/or third ion exchange steps;

FIG. 20 is a graph showing the stress profiles of Examples 6A-1 through6A-6 as a function of depth;

FIG. 21 is a graph showing the CT and DOC values of Examples 6A-1through 6A-6 as a function of ion exchange time;

FIG. 22 is a graph showing the stress profiles of Examples 6B-1 through6B-6 as a function of depth;

FIG. 23 is a graph showing the CT and DOC values of Examples 6B-1through 6B-6 as a function of ion exchange time;

FIG. 24 is a graph showing the stress profiles of Examples 6C-1 through6C-6 as a function of depth;

FIG. 25 is a graph showing the CT and DOC values of Examples 6C-1through 6C-6 as a function of ion exchange time;

FIG. 26 is a graph showing the stress profiles of Examples 6D-1 through6D-6 as a function of depth;

FIG. 27 is a graph showing the CT and DOC values of Examples 6D-1through 6D-6 as a function of ion exchange time;

FIG. 28 is a graph showing CT as a function of ion exchange time forExamples 7A-7G;

FIG. 29 is a graph showing the change in central tension values andstored tensile energy, both as a function of ion exchange time forExamples 7A-7G;

FIG. 30 is a graph showing the stress profiles of Comparative Example 8Aand Example 8B as a function of depth;

FIG. 31 is a graph showing the stored tensile energy of ComparativeExample 8A and Example 8B as a function of CT; and

FIG. 32 is a graph showing stored tensile energy of Comparative Example8C and Example 8D as a function of CT.

FIG. 33 is a graph showing the drop height failure for Examples 2, 6 and9B and Comparative Example 9I;

FIG. 34 is a graph showing the abraded ring-on-ring results for Examples2, 6, 9B and Comparative Example 9J;

FIG. 35 is a Weibull distribution plot showing the 4-point bend resultsfor Examples 2 and 9B;

FIG. 36 is a schematic cross-sectional view of an embodiment of theapparatus that is used to perform the inverted ball on sandpaper (IBoS)test described in the present disclosure;

FIG. 37 is a schematic cross-sectional representation of the dominantmechanism for failure due to damage introduction plus bending thattypically occurs in glass-based articles that are used in mobile or handheld electronic devices;

FIG. 38 is a flow chart for a method of conducting the IBoS test in theapparatus described herein; and

FIG. 39 is a graph illustrating various stress profiles according to oneor more embodiments of this disclosure.

DETAILED DESCRIPTION

Reference will now be made in detail to various embodiments, examples ofwhich are illustrated in the accompanying examples and drawings.

In the following description, like reference characters designate likeor corresponding parts throughout the several views shown in thefigures. It is also understood that, unless otherwise specified, termssuch as “top,” “bottom,” “outward,” “inward,” and the like are words ofconvenience and are not to be construed as limiting terms. In addition,whenever a group is described as comprising at least one of a group ofelements and combinations thereof, it is understood that the group maycomprise, consist essentially of, or consist of any number of thoseelements recited, either individually or in combination with each other.Similarly, whenever a group is described as consisting of at least oneof a group of elements or combinations thereof, it is understood thatthe group may consist of any number of those elements recited, eitherindividually or in combination with each other. Unless otherwisespecified, a range of values, when recited, includes both the upper andlower limits of the range as well as any ranges therebetween. As usedherein, the indefinite articles “a,” “an,” and the correspondingdefinite article “the” mean “at least one” or “one or more,” unlessotherwise specified. It also is understood that the various featuresdisclosed in the specification and the drawings can be used in any andall combinations.

As used herein, the terms “glass-based article” and “glass-basedsubstrates” are used in their broadest sense to include any object madewholly or partly of glass. Glass-based articles include laminates ofglass and non-glass materials, laminates of glass and crystallinematerials, and glass-ceramics (including an amorphous phase and acrystalline phase). Unless otherwise specified, all compositions areexpressed in terms of mole percent (mol %).

It is noted that the terms “substantially” and “about” may be utilizedherein to represent the inherent degree of uncertainty that may beattributed to any quantitative comparison, value, measurement, or otherrepresentation. These terms are also utilized herein to represent thedegree by which a quantitative representation may vary from a statedreference without resulting in a change in the basic function of thesubject matter at issue. Thus, for example, a glass-based article thatis “substantially free of MgO” is one in which MgO is not actively addedor batched into the glass-based article, but may be present in verysmall amounts as a contaminant.

Referring to the drawings in general and to FIGS. 1-3 in particular, itwill be understood that the illustrations are for the purpose ofdescribing particular embodiments and are not intended to limit thedisclosure or appended claims thereto. The drawings are not necessarilyto scale, and certain features and certain views of the drawings may beshown exaggerated in scale or in schematic in the interest of clarityand conciseness.

As used herein, DOC refers to the depth at which the stress within theglass-based article changes compressive to tensile stress. At the DOC,the stress crosses from a positive (compressive) stress to a negative(tensile) stress (e.g., 130 in FIG. 1) and thus exhibits a stress valueof zero.

As used herein, the terms “chemical depth”, “chemical depth of layer”and “depth of chemical layer” may be used interchangeably and refer tothe depth at which an ion of the metal oxide or alkali metal oxide(e.g., the metal ion or alkali metal ion) diffuses into the glass-basedarticle and the depth at which the concentration of the ion reaches aminimum value, as determined by Electron Probe Micro-Analysis (EPMA) orGlow Discharge-Optival Emission Spectroscopy (GD-OES)). In particular,to assess the depth of Na₂O diffusion or Na+ ion concentration may bedetermined using EPMA and FSM (described in more detail below).

According to the convention normally used in the art, compression isexpressed as a negative (<0) stress and tension is expressed as apositive (>0) stress. Throughout this description, however, CS isexpressed as a positive or absolute value—i.e., as recited herein,CS=|CS|.

Described herein are thin, chemically strengthened glass-based articlesthat include glasses, such as silicate glasses includingalkali-containing glass, and glass-ceramics that may be used as a coverglass for mobile electronic devices and touch-enabled displays. Theglass-based articles may also be used in displays (or as displayarticles) (e.g., billboards, point of sale systems, computers,navigation systems, and the like), architectural articles (walls,fixtures, panels, windows, etc.), transportation articles (e.g., inautomotive applications, trains, aircraft, sea craft, etc.), appliances(e.g., washers, dryers, dishwashers, refrigerators and the like), or anyarticle that requires some fracture resistance.

In particular, the glass-based articles described herein are thin andexhibit stress profiles that are typically only achievable throughtempering thick glass articles (e.g., having a thickness of about 2 mmor 3 mm or greater). The glass-based articles exhibit unique stressprofiles along the thickness thereof. In some cases, the glass-basedarticles exhibit a greater surface CS than tempered glass articles. Inone or more embodiments, the glass-based articles exhibit a larger depthof the compression layer (in which the CS decreases and increases moregradually than known chemically strengthened glass-based articles) suchthe glass-based article exhibits substantially improved fractureresistance, even when the glass-based article or a device including thesame is dropped on a hard, rough surface. The glass-based articles ofone or more embodiments exhibit a greater maximum CT value than someknown chemically strengthened glass substrates.

CS and depth of compressive stress layer (“DOL”) are measured usingthose means known in the art. DOL is distinguished from DOC bymeasurement technique in that DOL is determined by surface stress meter(FSM) using commercially available instruments such as the FSM-6000,manufactured by Luceo Co., Ltd. (Tokyo, Japan), or the like, and methodsof measuring CS and depth of layer are described in ASTM 1422C-99,entitled “Standard Specification for Chemically Strengthened FlatGlass,” and ASTM 1279.19779 “Standard Test Method for Non-DestructivePhotoelastic Measurement of Edge and Surface Stresses in Annealed,Heat-Strengthened, and Fully-Tempered Flat Glass,” the contents of whichare incorporated herein by reference in their entirety. Surface stressmeasurements rely upon the accurate measurement of the stress opticalcoefficient (SOC), which is related to the birefringence of the glass.SOC in turn is measured by those methods that are known in the art, suchas fiber and four point bend methods, both of which are described inASTM standard C770-98 (2008), entitled “Standard Test Method forMeasurement of Glass Stress-Optical Coefficient,” the contents of whichare incorporated herein by reference in their entirety, and a bulkcylinder method.

For strengthened glass-based articles in which the CS layers extend todeeper depths within the glass-based article, the FSM technique maysuffer from contrast issues which affect the observed DOL value. Atdeeper DOL values, there may be inadequate contrast between the TE andTM spectra, thus making the calculation of the difference between TE andTM spectra—and determining the DOL—more difficult. Moreover, the FSMtechnique is incapable of determining the stress profile (i.e., thevariation of CS as a function of depth within the glass-based article).In addition, the FSM technique is incapable of determining the DOLresulting from the ion exchange of certain elements such as, forexample, sodium for lithium.

The techniques described below have been developed to yield moreaccurately determine the DOC and stress profiles for strengthenedglass-based articles.

In U.S. patent application Ser. No. 13/463,322, entitled “Systems AndMethods for Measuring the Stress Profile of Ion-Exchanged Glass(hereinafter referred to as “Roussev I”),” filed by Rostislav V. Roussevet al. on May 3, 2012, and claiming priority to U.S. Provisional PatentApplication No. 61/489,800, having the same title and filed on May 25,2011, two methods for extracting detailed and precise stress profiles(stress as a function of depth) of tempered or chemically strengthenedglass are disclosed. The spectra of bound optical modes for TM and TEpolarization are collected via prism coupling techniques, and used intheir entirety to obtain detailed and precise TM and TE refractive indexprofiles n_(TM)(z) and n_(TE)(z). The contents of the above applicationsare incorporated herein by reference in their entirety.

In one embodiment, the detailed index profiles are obtained from themode spectra by using the inverse Wentzel-Kramers-Brillouin (IWKB)method.

In another embodiment, the detailed index profiles are obtained byfitting the measured mode spectra to numerically calculated spectra ofpre-defined functional forms that describe the shapes of the indexprofiles and obtaining the parameters of the functional forms from thebest fit. The detailed stress profile S(z) is calculated from thedifference of the recovered TM and TE index profiles by using a knownvalue of the stress-optic coefficient (SOC):S(z)=[n _(TM)(z)−n _(TE)(z)]/SOC  (2).

Due to the small value of the SOC, the birefringence n_(TM)(z)−n_(TE)(z)at any depth z is a small fraction (typically on the order of 1%) ofeither of the indices n_(TM)(z) and n_(TE)(z). Obtaining stress profilesthat are not significantly distorted due to noise in the measured modespectra requires determination of the mode effective indices withprecision on the order of 0.00001 RIU. The methods disclosed in RoussevI further include techniques applied to the raw data to ensure such highprecision for the measured mode indices, despite noise and/or poorcontrast in the collected TE and TM mode spectra or images of the modespectra. Such techniques include noise-averaging, filtering, and curvefitting to find the positions of the extremes corresponding to the modeswith sub-pixel resolution.

Similarly, U.S. patent application Ser. No. 14/033,954, entitled“Systems and Methods for Measuring Birefringence in Glass andGlass-Ceramics (hereinafter “Roussev II”),” filed by Rostislav V.Roussev et al. on Sep. 23, 2013, and claiming priority to U.S.Provisional Application Ser. No. 61/706,891, having the same title andfiled on Sep. 28, 2012, discloses apparatus and methods for opticallymeasuring birefringence on the surface of glass and glass ceramics,including opaque glass and glass ceramics. Unlike Roussev I, in whichdiscrete spectra of modes are identified, the methods disclosed inRoussev II rely on careful analysis of the angular intensitydistribution for TM and TE light reflected by a prism-sample interfacein a prism-coupling configuration of measurements. The contents of theabove applications are incorporated herein by reference in theirentirety.

Hence, correct distribution of the reflected optical intensity vs. angleis much more important than in traditional prism-couplingstress-measurements, where only the locations of the discrete modes aresought. To this end, the methods disclosed in Roussev I and Roussev IIcomprise techniques for normalizing the intensity spectra, includingnormalizing to a reference image or signal, correction for nonlinearityof the detector, averaging multiple images to reduce image noise andspeckle, and application of digital filtering to further smoothen theintensity angular spectra. In addition, one method includes formation ofa contrast signal, which is additionally normalized to correct forfundamental differences in shape between TM and TE signals. Theaforementioned method relies on achieving two signals that are nearlyidentical and determining their mutual displacement with sub-pixelresolution by comparing portions of the signals containing the steepestregions. The birefringence is proportional to the mutual displacement,with a coefficient determined by the apparatus design, including prismgeometry and index, focal length of the lens, and pixel spacing on thesensor. The stress is determined by multiplying the measuredbirefringence by a known stress-optic coefficient.

In another disclosed method, derivatives of the TM and TE signals aredetermined after application of some combination of the aforementionedsignal conditioning techniques. The locations of the maximum derivativesof the TM and TE signals are obtained with sub-pixel resolution, and thebirefringence is proportional to the spacing of the above two maxima,with a coefficient determined as before by the apparatus parameters.

Associated with the requirement for correct intensity extraction, theapparatus comprises several enhancements, such as using alight-scattering surface (static diffuser) in close proximity to or onthe prism entrance surface to improve the angular uniformity ofillumination, a moving diffuser for speckle reduction when the lightsource is coherent or partially coherent, and light-absorbing coatingson portions of the input and output facets of the prism and on the sidefacets of the prism, to reduce parasitic background which tends todistort the intensity signal. In addition, the apparatus may include aninfrared light source to enable measurement of opaque materials.

Furthermore, Roussev II discloses a range of wavelengths and attenuationcoefficients of the studied sample, where measurements are enabled bythe described methods and apparatus enhancements. The range is definedby α_(s)λ<250πσ_(s), where α_(s) is the optical attenuation coefficientat measurement wavelength λ, and σ_(s) is the expected value of thestress to be measured with typically required precision for practicalapplications. This wide range allows measurements of practicalimportance to be obtained at wavelengths where the large opticalattenuation renders previously existing measurement methodsinapplicable. For example, Roussev II discloses successful measurementsof stress-induced birefringence of opaque white glass-ceramic at awavelength of 1550 nm, where the attenuation is greater than about 30dB/mm.

While it is noted above that there are some issues with the FSMtechnique at deeper DOL values, FSM is still a beneficial conventionaltechnique which may utilized with the understanding that an error rangeof up to +/−20% is possible at deeper DOL values. DOL as used hereinrefers to depths of the compressive stress layer values computed usingthe FSM technique, whereas DOC refer to depths of the compressive stresslayer determined by the methods described in Roussev I & II.

As stated above, the glass-based articles described herein may bechemically strengthened by ion exchange and exhibit stress profiles thatare distinguished from those exhibited by known strengthened glass. Inthis process, ions at or near the surface of the glass-based article arereplaced by—or exchanged with—larger ions having the same valence oroxidation state. In those embodiments in which the glass-based articlecomprises an alkali aluminosilicate glass, ions in the surface layer ofthe glass and the larger ions are monovalent alkali metal cations, suchas Li⁺ (when present in the glass-based article), Na⁺, K⁺, Rb⁺, and Cs⁺.Alternatively, monovalent cations in the surface layer may be replacedwith monovalent cations other than alkali metal cations, such as Ag⁺ orthe like.

Ion exchange processes are typically carried out by immersing aglass-based article in a molten salt bath (or two or more molten saltbaths) containing the larger ions to be exchanged with the smaller ionsin the glass-based article. It should be noted that aqueous salt bathsmay also be utilized. In addition, the composition of the bath(s) mayinclude more than one type of larger ion (e.g., Na+ and K+) or a singlelarger ion. It will be appreciated by those skilled in the art thatparameters for the ion exchange process, including, but not limited to,bath composition and temperature, immersion time, the number ofimmersions of the glass-based article in a salt bath (or baths), use ofmultiple salt baths, additional steps such as annealing, washing, andthe like, are generally determined by the composition of the glass-basedarticle (including the structure of the article and any crystallinephases present) and the desired DOL or DOC and CS of the glass-basedarticle that result from the strengthening operation. By way of example,ion exchange of glass-based articles may be achieved by immersion of theglass-based articles in at least one molten bath containing a salt suchas, but not limited to, nitrates, sulfates, and chlorides of the largeralkali metal ion. Typical nitrates include KNO₃, NaNO₃, LiNO₃, NaSO₄ andcombinations thereof. The temperature of the molten salt bath typicallyis in a range from about 380° C. up to about 450° C., while immersiontimes range from about 15 minutes up to about 100 hours depending onglass thickness, bath temperature and glass diffusivity. However,temperatures and immersion times different from those described abovemay also be used.

In one or more embodiments, the glass-based articles may be immersed ina molten salt bath of 100% NaNO₃ having a temperature from about 370° C.to about 480° C. In some embodiments, the glass-based substrate may beimmersed in a molten mixed salt bath including from about 5% to about90% KNO₃ and from about 10% to about 95% NaNO₃. In some embodiments, theglass-based substrate may be immersed in a molten mixed salt bathincluding Na₂SO₄ and NaNO₃ and have a wider temperature range (e.g., upto about 500° C.). In one or more embodiments, the glass-based articlemay be immersed in a second bath, after immersion in a first bath.Immersion in a second bath may include immersion in a molten salt bathincluding 100% KNO₃ for 15 minutes to 8 hours.

Ion exchange conditions can be tailored to provide a “spike” or toincrease the slope of the stress profile at or near the surface. Thisspike can be achieved by single bath or multiple baths, with the bath(s)having a single composition or mixed composition, due to the uniqueproperties of the glass compositions used in the glass-based articlesdescribed herein.

As illustrated in FIG. 3, the glass-based article 300 of one or moreembodiments includes a first surface 302 and a second surface 304opposing the first surface, defining a thickness t. In one or moreembodiments, the thickness t may be about 3 millimeter or less (e.g., inthe range from about 0.01 millimeter to about 3 millimeter, from about0.1 millimeter to about 3 millimeter, from about 0.2 millimeter to about3 millimeter, from about 0.3 millimeter to about 3 millimeter, fromabout 0.4 millimeter to about 3 millimeter, from about 0.01 millimeterto about 2.5 millimeter, from about 0.01 millimeter to about 2millimeter, from about 0.01 millimeter to about 1.5 millimeter, fromabout 0.01 millimeter to about 1 millimeter, from about 0.01 millimeterto about 0.9 millimeter, from about 0.01 millimeter to about 0.8millimeter, from about 0.01 millimeter to about 0.7 millimeter, fromabout 0.01 millimeter to about 0.6 millimeter, from about 0.01millimeter to about 0.5 millimeter, from about 0.1 millimeter to about0.5 millimeter, or from about 0.3 millimeter to about 0.5 millimeter.)

The glass-based article includes a stress profile that extends from thefirst surface 302 to the second surface 304 (or along the entire lengthof the thickness t). In the embodiment shown in FIG. 3, the stressprofile 312 as measured by Roussev I & II as described herein is shownalong with the stress profile 340 estimated by FSM measurementtechniques as described herein. The x-axis represents the stress valueand the y-axis represents the thickness or depth within the glass-basedarticle.

As illustrated in FIG. 3, the stress profile 312 exhibits a CS layer 315(with a surface CS 310), a CT layer 325 (with a maximum CT 320) and aDOC 317 at which the stress profile 312 turns from compressive totensile at 330. The CT layer 325 also has an associated depth or length327 (CT region or layer). The estimated stress profile 340 exhibits aDOL that is greater than the DOC. As used herein, reference to the DOCand DOL is with respect to each depth from one surface (either the firstsurface 302 or the second surface 304), with the understanding that suchDOC or DOL may also be present from the other surface.

The surface CS 310 may be about 150 MPa or greater or about 200 MPa orgreater (e.g., about 250 MPa or greater, about 300 MPa or greater, about400 MPa or greater, about 450 MPa or greater, about 500 MPa or greater,or about 550 MPa or greater). The surface CS 310 may be up to about 900MPa, up to about 1000 MPa, up to about 1100 MPa, or up to about 1200MPa. The maximum CT 320 may be about 25 MPa or greater, about 50 MPa orgreater or about 100 MPa or greater (e.g., about 150 MPa or greater,about 200 MPa or greater, 250 MPa or greater, or about 300 MPa orgreater). In some embodiments, the maximum CT 320 may be in the rangefrom about 50 MPa to about 250 MPa (e.g., from about 75 MPa to about 250MPa, from about 100 MPa to about 250 MPa, from about 150 MPa to about250 MPa, from about 50 MPa to about 175 MPa, from about 50 MPa to about150 MPa, or from about 50 MPa to about 100 MP). The maximum CT 320 maybe positioned at a range from about 0.3·t to about 0.7·t, from about0.4·t to about 0.6·t or from about 0.45·t to about 0.55·t. It should benoted that any one or more of surface CS 310 and maximum CT 320 may bedependent on the thickness of the glass-based article. For example,glass-based articles having at thickness of about 0.8 mm may have amaximum CT of about 100 MPa or greater. When the thickness of theglass-based article decreases, the maximum CT may increase. In otherwords, the maximum CT increases with decreasing thickness (or as theglass-based article becomes thinner).

In some embodiments, the ratio of the maximum CT 320 to the surface CS310 in the range from about 0.05 to about 1 (e.g., in the range fromabout 0.05 to about 0.5, from about 0.05 to about 0.3, from about 0.05to about 0.2, from about 0.05 to about 0.1, from about 0.5 to about 0.8,from about 0.0.5 to about 1, from about 0.2 to about 0.5, from about 0.3to about 0.5). In known chemically strengthened glass-based articles,the ratio of the maximum CT 320 to the surface CS 310 is 0.1 or less. Insome embodiments, surface CS may be 1.5 times (or 2 times or 2.5 times)the maximum CT or greater. In some embodiments, the surface CS may be upto about 20 times the maximum CT.

In one or more embodiments, the stress profile 312 comprises a maximumCS, which is typically the surface CS 310, which can be found at one orboth of the first surface 302 and the second surface 304. In one or moreembodiments, the CS layer or region 315 extends along a portion of thethickness to the DOC 317 and a maximum CT 320. In one or moreembodiments, the DOC 317 may be about 0.1·t or greater. For example, theDOC 317 may be about 0.12·t or greater, about 0.14·t or greater, about0.15·t or greater, about 0.16·t or greater, 0.17·t or greater, 0.18·t orgreater, 0.19·t or greater, 0.20·t or greater, about 0.21·t or greater,or up to about 0.25·t. In some embodiments, the DOC 317 is less than thechemical depth 342. The chemical depth 342 may be about 0.4·t orgreater, 0.5·t or greater, about 55·t or greater, or about 0.6·t orgreater. In one or more embodiments, the stress profile 312 may bedescribed as parabolic-like in shape. In some embodiments, the stressprofile along the region or depth of the glass-based article exhibitingtensile stress exhibits a parabolic-like shape. In one or more specificembodiments, the stress profile 312 is free of a flat stress (i.e.,compressive or tensile) portion or a portion that exhibits asubstantially constant stress (i.e., compressive or tensile). In someembodiments, the CT region exhibits a stress profile that issubstantially free of a flat stress or free of a substantially constantstress. In one or more embodiments, all points of the stress profile 312between a thickness range from about 0t up to about 0.2·t and greaterthan 0.8·t (or from about 0·t to about 0.3·t and greater than 0.7.0comprise a tangent that is less than about −0.1 MPa/micrometers orgreater than about 0.1 MPa/micrometers. In some embodiments, the tangentmay be less than about −0.2 MPa/micrometers or greater than about 0.2MPa/micrometers. In some more specific embodiments, the tangent may beless than about −0.3 MPa/micrometers or greater than about 0.3MPa/micrometers. In an even more specific embodiment, the tangent may beless than about −0.5 MPa/micrometers or greater than about 0.5MPa/micrometers. In other words, the stress profile of one or moreembodiments along these thickness ranges (i.e., 0·t up to about 2·t andgreater than 0.8t, or from about 0t to about 0.3·t and 0.7·t or greater)exclude points having a tangent, as described herein. Without beingbound by theory, known error function or quasi-linear stress profileshave points along these thickness ranges (i.e., 0·t up to about 2·t andgreater than 0.8·t, or from about 0·t to about 0.3·t and 0.7·t orgreater) that have a tangent that is from about −0.1 MPa/micrometers toabout 0.1 MPa/micrometers, from about −0.2 MPa/micrometers to about 0.2MPa/micrometers, from about −0.3 MPa/micrometers to about 0.3MPa/micrometers, or from about −0.5 MPa/micrometers to about 0.5MPa/micrometers (indicating a flat or zero slope stress profile alongsuch thickness ranges, as shown in FIG. 2, 220). The stress profiles ofone or more embodiments of this disclosure do not exhibit such a stressprofile having a flat or zero slope stress profile along these thicknessranges, as shown in FIG. 3.

In one or more embodiments, the glass-based article exhibits a stressprofile a thickness range from about 0.1·t to 0.3·t and from about 0.7·tto 0.9·t that comprises a maximum tangent and a minimum tangent. In someinstances, the difference between the maximum tangent and the minimumtangent is about 3.5 MPa/micrometers or less, about 3 MPa/micrometers orless, about 2.5 MPa/micrometers or less, or about 2 MPa/micrometers orless.

In one or more embodiments, the stress profile 312 is substantially freeof any linear segments that extend in a depth direction or along atleast a portion of the thickness t of the glass-based article. In otherwords, the stress profile 312 is substantially continuously increasingor decreasing along the thickness t. In some embodiments, the stressprofile is substantially free of any linear segments in a depthdirection having a length of about 10 micrometers or more, about 50micrometers or more, or about 100 micrometers or more, or about 200micrometers or more. As used herein, the term “linear” refers to a slopehaving a magnitude of less than about 5 MPa/micrometer, or less thanabout 2 MPa/micrometer along the linear segment. In some embodiments,one or more portions of the stress profile that are substantially freeof any linear segments in a depth direction are present at depths withinthe glass-based article of about 5 micrometers or greater (e.g., 10micrometers or greater, or 15 micrometers or greater) from either one orboth the first surface or the second surface. For example, along a depthof about 0 micrometers to less than about 5 micrometers from the firstsurface, the stress profile may include linear segments, but from adepth of about 5 micrometers or greater from the first surface, thestress profile may be substantially free of linear segments.

In some embodiments, the stress profile may include linear segments atdepths from about 0t up to about 0.1t and may be substantially free oflinear segments at depths of about 0.1t to about 0.4t. In someembodiments, the stress profile from a thickness in the range from about0t to about 0.1t may have a slope in the range from about 20 MPa/micronsto about 200 MPa/microns. As will be described herein, such embodimentsmay be formed using a single ion-exchange process by which the bathincludes two or more alkali salts or is a mixed alkali salt bath ormultiple (e.g., 2 or more) ion exchange processes.

In one or more embodiments, the glass-based article may be described interms of the shape of the stress profile along the CT region (327 inFIG. 3). For example, in some embodiments, the stress profile along theCT region (where stress is in tension) may be approximated by equation.In some embodiments, the stress profile along the CT region may beapproximated by equation (1):Stress(x)=MaxCT−(((MaxCT·(n+1))/0.5^(n))·|(x/t)−0.5|^(n))  (1)In equation (1), the stress (x) is the stress value at position x. Herethe stress is positive (tension). MaxCT is the maximum central tensionas a positive value in MPa. The value x is position along the thickness(t) in micrometers, with a range from 0 to t; x=0 is one surface (302,in FIG. 3), x=0.5t is the center of the glass-based article,stress(x)=MaxCT, and x=t is the opposite surface (304, in FIG. 3). MaxCTused in equation (1) may be in the range from about 50 MPa to about 350MPa (e.g., 60 MPa to about 300 MPa, or from about 70 MPa to about 270MPa), and n is a fitting parameter from 1.5 to 5 (e.g., 2 to 4, 2 to 3or 1.8 to 2.2) whereby n=2 can provide a parabolic stress profile,exponents that deviate from n=2 provide stress profiles with nearparabolic stress profiles. FIG. 39 shows illustrative stress profilesfor different combinations of MaxCT and n (from 1.5 to 5 as indicated inthe legend), for a glass-based article having a thickness of 0.8 mm.

In some embodiments, the stress profile may be modified by heattreatment. In such embodiments, the heat treatment may occur before anyion-exchange processes, between ion-exchange processes, or after allion-exchange processes. In some embodiments, the heat treatment mayresult reduce the slope of the stress profile at or near the surface. Insome embodiments, where a steeper or greater slope is desired at thesurface, an ion-exchange process after the heat treatment may beutilized to provide a “spike” or to increase the slope of the stressprofile at or near the surface.

In one or more embodiments, the stress profile 312 (and/or estimatedstress profile 340) is generated due to a non-zero concentration of ametal oxide(s) that varies along a portion of the thickness. Thevariation in concentration may be referred to herein as a gradient. Insome embodiments, the concentration of a metal oxide is non-zero andvaries, both along a thickness range from about 0·t to about 0.3·t. Insome embodiments, the concentration of the metal oxide is non-zero andvaries along a thickness range from about 0·t to about 0.35·t, fromabout 0·t to about 0.4·t, from about 0·t to about 0.45·t or from about0·t to about 0.48·t. The metal oxide may be described as generating astress in the glass-based article. The variation in concentration may becontinuous along the above-referenced thickness ranges. Variation inconcentration may include a change in metal oxide concentration of about0.2 mol % along a thickness segment of about 100 micrometers. Thischange may be measured by known methods in the art including microprobe,as shown in Example 1. The metal oxide that is non-zero in concentrationand varies along a portion of the thickness may be described asgenerating a stress in the glass-based article.

The variation in concentration may be continuous along theabove-referenced thickness ranges. In some embodiments, the variation inconcentration may be continuous along thickness segments in the rangefrom about 10 micrometers to about 30 micrometers. In some embodiments,the concentration of the metal oxide decreases from the first surface toa point between the first surface and the second surface and increasesfrom the point to the second surface.

The concentration of metal oxide may include more than one metal oxide(e.g., a combination of Na₂O and K₂O). In some embodiments, where twometal oxides are utilized and where the radius of the ions differ fromone or another, the concentration of ions having a larger radius isgreater than the concentration of ions having a smaller radius atshallow depths, while the at deeper depths, the concentration of ionshaving a smaller radius is greater than the concentration of ions havinglarger radius. For example, where a single Na− and K− containing bath isused in the ion exchange process, the concentration of K+ ions in theglass-based article is greater than the concentration of Na+ ions atshallower depths, while the concentration of Na+ is greater than theconcentration of K+ ions at deeper depths. This is due, in part, due tothe size of the ions. In such glass-based articles, the area at or nearthe surface comprises a greater CS due to the greater amount of largerions at or near the surface. This greater CS may be exhibited by astress profile having a steeper slope at or near the surface (i.e., aspike in the stress profile at the surface).

The concentration gradient or variation of one or more metal oxides iscreated by chemically strengthening the glass-based article, forexample, by the ion exchange processes previously described herein, inwhich a plurality of first metal ions in the glass-based article isexchanged with a plurality of second metal ions. The first ions may beions of lithium, sodium, potassium, and rubidium. The second metal ionsmay be ions of one of sodium, potassium, rubidium, and cesium, with theproviso that the second alkali metal ion has an ionic radius greaterthan the ionic radius than the first alkali metal ion. The second metalion is present in the glass-based substrate as an oxide thereof (e.g.,Na₂O, K₂O, Rb₂O, Cs₂O or a combination thereof).

In one or more embodiments, the metal oxide concentration gradientextends through a substantial portion of the thickness t or the entirethickness t of the glass-based article, including the CT layer 325. Inone or more embodiments, the concentration of the metal oxide is about0.5 mol % or greater in the CT layer 325. In some embodiments, theconcentration of the metal oxide may be about 0.5 mol % or greater(e.g., about 1 mol % or greater) along the entire thickness of theglass-based article, and is greatest at the first surface 302 and/or thesecond surface 304 and decreases substantially constantly to a pointbetween the first surface 302 and the second surface 304. At that point,the concentration of the metal oxide is the least along the entirethickness t; however the concentration is also non-zero at that point.In other words, the non-zero concentration of that particular metaloxide extends along a substantial portion of the thickness t (asdescribed herein) or the entire thickness t. In some embodiments, thelowest concentration in the particular metal oxide is in the CT layer327. The total concentration of the particular metal oxide in theglass-based article may be is in the range from about 1 mol % to about20 mol %.

In one or more embodiments, the glass-based article includes a firstmetal oxide concentration and a second metal oxide concentration, suchthat the first metal oxide concentration is in the range from about 0mol % to about 15 mol % along a first thickness range from about 0t toabout 0.5t, and the second metal oxide concentration is in the rangefrom about 0 mol % to about 10 mol % from a second thickness range fromabout 0 micrometers to about 25 micrometers (or from about 0 micrometersto about 12 micrometers). The glass-based article may include anoptional third metal oxide concentration. The first metal oxide mayinclude Na₂O while the second metal oxide may include K2O.

The concentration of the metal oxide may be determined from a baselineamount of the metal oxide in the glass-based article prior to beingmodified to include the concentration gradient of such metal oxide.

In one or more embodiments, the glass-based articles may be described interms of how they fracture and the fragments that result from suchfracture. In one or more embodiments, when fractured, the glass-basedarticles fracture into 2 or more fragments per square inch (or per6.4516 square centimeters) of the glass-based article (prior tofracture). In some cases, the glass-based articles fracture into 3 ormore, 4 or more, 5 or more, or 10 or more fragments per square inch (orper 6.4516 square centimeters) of the glass-based article (prior tofracture). In some instances, when fractured, the glass-based articlesfracture in to fragments such that 50% or more of the fragments have asurface area that is less than 5%, less than 2%, or less than 1% of thesurface area of the glass-based article (prior to fracture). In someembodiments, when fractured, the glass-based articles fracture in tofragments such that 90% or more or even 100% of the fragments have asurface area that is less than 5%, less than 2%, or less than 1% of thesurface area of the glass-based article (prior to fracture).

In one or more embodiments, after chemically strengthening theglass-based article, the resulting stress profile 317 (and estimatedstress profile 340) of the glass-based article provides improvedfracture resistance. For example, in some embodiments, upon fracture,the glass-based article comprises fragments having an average longestcross-sectional dimension of less than or equal to about 2·t (e.g.,1.8·t, 1.6·t, 1.5·t, 1.4·t, 1.2·t or 1·t or less).

In one or more embodiments, the glass-based articles may exhibit afracture toughness (K_(1C)) of about 0.7 MPa·m^(1/2) or greater. In somecases, the fracture toughness may be about 0.8 MPa·m^(1/2) or greater,or about 0.9 MPa·m^(1/2) or greater. In some embodiments the fracturetoughness may be in the range from about 0.7 MPa·m^(1/2) to about 1MPa·m^(1/2).

In some embodiments, the substrate may also be characterized as having ahardness from about 500 HVN to about 800 HVN, as measured by Vickershardness test at a load of 200 g.

The glass-based articles described herein may exhibit a stored tensileenergy in the range from greater than 0 J/m² to about 20 J/m². In someinstances, the stored tensile energy may be in the range from about 1J/m² to about 20 J/m², from about 2 J/m² to about 20 J/m², from about 3J/m² to about 20 J/m², from about 4 J/m² to about 20 J/m², from about 1J/m² to about 19 J/m², from about 1 J/m² to about 18 J/m², from about 1J/m² to about 16 J/m², from about 4 J/m² to about 20 J/m², or from about4 J/m² to about 18 J/m². The stored tensile energy is calculated byintegrating in the tensile region the stored elastic energy Σ per unitarea of specimen of thickness t using Equation (2):Σ=0.5σ² t/E  (2)in which σ is stress and E is young's modulus.

More specifically, stored tensile energy is calculated using thefollowing Equation (3):stored tensile energy (J/m²)=1−v/2E∫σ^2dt  (3)where n is Poisson's ratio, E is the elastic modulus and the integrationis computed for the tensile region only.

In one or more embodiments, the glass-based articles exhibit improvedsurface strength when subjected to abraded ring-on-ring (AROR) testing.The strength of a material is defined as the stress at which fractureoccurs. The A-ROR test is a surface strength measurement for testingflat glass specimens, and ASTM C1499-09(2013), entitled “Standard TestMethod for Monotonic Equibiaxial Flexural Strength of Advanced Ceramicsat Ambient Temperature,” serves as the basis for the ring-on-ringabraded ROR test methodology described herein. The contents of ASTMC1499-09 are incorporated herein by reference in their entirety. In oneembodiment, the glass specimen is abraded prior to ring-on-ring testingwith 90 grit silicon carbide (SiC) particles that are delivered to theglass sample using the method and apparatus described in Annex A2,entitled“abrasion Procedures,” of ASTM C158-02(2012), entitled “StandardTest Methods for Strength of Glass by Flexure (Determination of Modulusof Rupture). The contents of ASTM C158-02 and the contents of Annex 2 inparticular are incorporated herein by reference in their entirety.

Prior to ring-on-ring testing a surface of the glass-based article isabraded as described in ASTM C158-02, Annex 2, to normalize and/orcontrol the surface defect condition of the sample using the apparatusshown in Figure A2.1 of ASTM C158-02. The abrasive material is typicallysandblasted onto the surface 110 of the glass-based article at a load of15 psi using an air pressure of 304 kPa (44 psi); although in theExamples below, the abrasive material was sandblasted onto the surface110 at a load of 25 psi and 45 psi. After air flow is established, 5 cm³of abrasive material is dumped into a funnel and the sample issandblasted for 5 seconds after introduction of the abrasive material.

For the ring-on-ring test, a glass-based article having at least oneabraded surface 410 as shown in FIG. 4 is placed between two concentricrings of differing size to determine equibiaxial flexural strength(i.e., the maximum stress that a material is capable of sustaining whensubjected to flexure between two concentric rings), as also shown inFIG. 4. In the abraded ring-on-ring configuration 400, the abradedglass-based article 410 is supported by a support ring 420 having adiameter D2. A force F is applied by a load cell (not shown) to thesurface of the glass-based article by a loading ring 430 having adiameter D1.

The ratio of diameters of the loading ring and support ring D1/D2 may bein a range from about 0.2 to about 0.5. In some embodiments, D1/D2 isabout 0.5. Loading and support rings 130, 120 should be alignedconcentrically to within 0.5% of support ring diameter D2. The load cellused for testing should be accurate to within ±1% at any load within aselected range. In some embodiments, testing is carried out at atemperature of 23±2° C. and a relative humidity of 40±10%.

For fixture design, the radius r of the protruding surface of theloading ring 430, h/2≤r≤3h/2, where his the thickness of glass-basedarticle 410. Loading and support rings 430, 420 are typically made ofhardened steel with hardness HRc>40. ROR fixtures are commerciallyavailable.

The intended failure mechanism for the ROR test is to observe fractureof the glass-based article 410 originating from the surface 430 a withinthe loading ring 430. Failures that occur outside of this region—i.e.,between the loading rings 430 and support rings 420—are omitted fromdata analysis. Due to the thinness and high strength of the glassglass-based article 410, however, large deflections that exceed ½ of thespecimen thickness h are sometimes observed. It is therefore notuncommon to observe a high percentage of failures originating fromunderneath the loading ring 430. Stress cannot be accurately calculatedwithout knowledge of stress development both inside and under the ring(collected via strain gauge analysis) and the origin of failure in eachspecimen. AROR testing therefore focuses on peak load at failure as themeasured response.

The strength of glass-based article depends on the presence of surfaceflaws. However, the likelihood of a flaw of a given size being presentcannot be precisely predicted, as the strength of glass is statisticalin nature. A probability distribution can therefore generally be used asa statistical representation of the data obtained.

In some embodiments, the strengthened glass-based articles describedherein has a surface or equibiaxial flexural strength of at least 20 kgfand up to about 30 kgf as determined by abraded ring-on-ring testingusing a load of 25 psi or even 45 psi to abrade the surface. In otherembodiments, the surface strength is at least 25 kgf, and in still otherembodiments, at least 30 kgf.

In some embodiments, the strengthened glass-based articles describedherein may be described in terms of performance in an inverted ball onsandpaper (IBoS) test. The IBoS test is a dynamic component level testthat mimics the dominant mechanism for failure due to damageintroduction plus bending that typically occurs in glass-based articlesthat are used in mobile or hand held electronic devices, asschematically shown in FIG. 36. In the field, damage introduction (a inFIG. 37) occurs on the top surface of the glass-based article. Fractureinitiates on the top surface of the glass-based article and damageeither penetrates the glass-based article (b in FIG. 37) or the fracturepropagates from bending on the top surface or from the interior portionsof the glass-based article (c in FIG. 37). The IBoS test is designed tosimultaneously introduce damage to the surface of the glass and applybending under dynamic load. In some instances, the glass-based articleexhibits improved drop performance when it includes a compressive stressthan if the same glass-based article does not include a compressivestress.

An IBoS test apparatus is schematically shown in FIG. 36. Apparatus 500includes a test stand 510 and a ball 530. Ball 530 is a rigid or solidball such as, for example, a stainless steel ball, or the like. In oneembodiment, ball 530 is a 4.2 gram stainless steel ball having diameterof 10 mm. The ball 530 is dropped directly onto the glass-based articlesample 518 from a predetermined height h. Test stand 510 includes asolid base 512 comprising a hard, rigid material such as granite or thelike. A sheet 514 having an abrasive material disposed on a surface isplaced on the upper surface of the solid base 512 such that surface withthe abrasive material faces upward. In some embodiments, sheet 514 issandpaper having a 30 grit surface and, in other embodiments, a 180 gritsurface. The glass-based article sample 518 is held in place above sheet514 by sample holder 515 such that an air gap 516 exists betweenglass-based article sample 518 and sheet 514. The air gap 516 betweensheet 514 and glass-based article sample 518 allows the glass-basedarticle sample 518 to bend upon impact by ball 530 and onto the abrasivesurface of sheet 514. In one embodiment, the glass-based article sample218 is clamped across all corners to keep bending contained only to thepoint of ball impact and to ensure repeatability. In some embodiments,sample holder 514 and test stand 510 are adapted to accommodate samplethicknesses of up to about 2 mm. The air gap 516 is in a range fromabout 50 μm to about 100 μm. Air gap 516 is adapted to adjust fordifference of material stiffness (Young's modulus, Emod), but alsoincludes the elastic modulus and thickness of the sample. An adhesivetape 520 may be used to cover the upper surface of the glass-basedarticle sample to collect fragments in the event of fracture of theglass-based article sample 518 upon impact of ball 530.

Various materials may be used as the abrasive surface. In a oneparticular embodiment, the abrasive surface is sandpaper, such assilicon carbide or alumina sandpaper, engineered sandpaper, or anyabrasive material known to those skilled in the art for havingcomparable hardness and/or sharpness. In some embodiments, sandpaperhaving 30 grit may be used, as it has a surface topography that is moreconsistent than either concrete or asphalt, and a particle size andsharpness that produces the desired level of specimen surface damage.

In one aspect, a method 600 of conducting the IBoS test using theapparatus 500 described hereinabove is shown in FIG. 38. In Step 610, aglass-based article sample (218 in FIG. 36) is placed in the test stand510, described previously and secured in sample holder 515 such that anair gap 516 is formed between the glass-based article sample 518 andsheet 514 with an abrasive surface. Method 600 presumes that the sheet514 with an abrasive surface has already been placed in test stand 510.In some embodiments, however, the method may include placing sheet 514in test stand 510 such that the surface with abrasive material facesupward. In some embodiments (Step 610 a), an adhesive tape 520 isapplied to the upper surface of the glass-based article sample 518 priorto securing the glass-based article sample 518 in the sample holder 510.

In Step 520, a solid ball 530 of predetermined mass and size is droppedfrom a predetermined height h onto the upper surface of the glass-basedarticle sample 518, such that the ball 530 impacts the upper surface (oradhesive tape 520 affixed to the upper surface) at approximately thecenter (i.e., within 1 mm, or within 3 mm, or within 5 mm, or within 10mm of the center) of the upper surface. Following impact in Step 520,the extent of damage to the glass-based article sample 518 is determined(Step 630). As previously described hereinabove, herein, the term“fracture” means that a crack propagates across the entire thicknessand/or entire surface of a substrate when the substrate is dropped orimpacted by an object.

In method 600, the sheet 518 with the abrasive surface may be replacedafter each drop to avoid “aging” effects that have been observed inrepeated use of other types (e.g., concrete or asphalt) of drop testsurfaces.

Various predetermined drop heights h and increments are typically usedin method 600. The test may, for example, utilize a minimum drop heightto start (e.g., about 10-20 cm). The height may then be increased forsuccessive drops by either a set increment or variable increments. Thetest described in method 600 is stopped once the glass-based articlesample 518 breaks or fractures (Step 631). Alternatively, if the dropheight h reaches the maximum drop height (e.g., about 100 cm) withoutfracture, the drop test of method 300 may also be stopped, or Step 520may be repeated at the maximum height until fracture occurs.

In some embodiments, IBoS test of method 600 is performed only once oneach glass-based article sample 518 at each predetermined height h. Inother embodiments, however, each sample may be subjected to multipletests at each height.

If fracture of the glass-based article sample 518 has occurred (Step 631in FIG. 38), the IBoS test according to method 600 is ended (Step 640).If no fracture resulting from the ball drop at the predetermined dropheight is observed (Step 632), the drop height is increased by apredetermined increment (Step 634)—such as, for example 5, 10, or 20cm—and Steps 620 and 630 are repeated until either sample fracture isobserved (631) or the maximum test height is reached (636) withoutsample fracture. When either Step 631 or 636 is reached, the testaccording to method 600 is ended.

When subjected to the inverted ball on sandpaper (IBoS) test describedabove, embodiments of the glass-based article described herein have atleast about a 60% survival rate when the ball is dropped onto thesurface of the glass from a height of 100 cm. For example, a glass-basedarticle is described as having a 60% survival rate when dropped from agiven height when three of five identical (or nearly identical) samples(i.e., having approximately the same composition and, when strengthened,approximately the same compressive stress and depth of compression orcompressive stress layer, as described herein) survive the IBoS droptest without fracture when dropped from the prescribed height (here 100cm). In other embodiments, the survival rate in the 100 cm IBoS test ofthe glass-based articles that are strengthened is at least about 70%, inother embodiments, at least about 80%, and, in still other embodiments,at least about 90%. In other embodiments, the survival rate of thestrengthened glass-based articles dropped from a height of 100 cm in theIBoS test is at least about 60%, in other embodiments, at least about70%, in still other embodiments, at least about 80%, and, in otherembodiments, at least about 90%. In one or more embodiments, thesurvival rate of the strengthened glass-based articles dropped from aheight of 150 cm in the IBoS test is at least about 60%, in otherembodiments, at least about 70%, in still other embodiments, at leastabout 80%, and, in other embodiments, at least about 90%.

To determine the survivability rate of the glass-based articles whendropped from a predetermined height using the IBoS test method andapparatus described hereinabove, at least five identical (or nearlyidentical) samples (i.e., having approximately the same composition and,if strengthened, approximately the same compressive stress and depth ofcompression or layer) of the glass-based articles are tested, althoughlarger numbers (e.g., 10, 20, 30, etc.) of samples may be subjected totesting to raise the confidence level of the test results. Each sampleis dropped a single time from the predetermined height (e.g., 100 cm or150 cm) or, alternatively, dropped from progressively higher heightswithout fracture until the predetermined height is reached, and visually(i.e., with the naked eye) examined for evidence of fracture (crackformation and propagation across the entire thickness and/or entiresurface of a sample). A sample is deemed to have “survived” the droptest if no fracture is observed after being dropped from thepredetermined height, and a sample is deemed to have “failed (or “notsurvived”) if fracture is observed when the sample is dropped from aheight that is less than or equal to the predetermined height. Thesurvivability rate is determined to be the percentage of the samplepopulation that survived the drop test. For example, if 7 samples out ofa group of 10 did not fracture when dropped from the predeterminedheight, the survivability rate of the glass would be 70%.

The glass-based articles described herein may be transparent or opaque.In one or more the glass-based article may have a thickness of about 1millimeter or less and exhibit a transmittance of about 88% or greaterover a wavelength in the range from about 380 nm to about 780 nm. Inanother embodiment, the glass-based article may have a thickness ofabout 1 millimeter or less and exhibit a transmittance of about 10% orless over a wavelength in the range from about 380 nm to about 780 nm.

The glass-based article may also exhibit a substantially white color.For example, the glass-based article may exhibit CIELAB color spacecoordinates, under a CIE illuminant F02, of L* values of about 88 andgreater, a* values in the range from about −3 to about +3, and b* valuesin the range from about −6 to about +6. Alternatively, the glass-basedarticle may exhibit CIELAB color space coordinates, under a CIEilluminant F02, of L* values of about 40 and less, a* values in therange from about −3 to about +3, and b* values in the range from about−6 to about +6. Such color space coordinates may be present under otherCIE illuminants (e.g., D65).

Choice of substrates not particularly limited. In some examples, theglass-based article may be described as having a high cation diffusivityfor ion exchange. In one or more embodiments, the glass or glass-ceramichas fast ion-exchange capability, i.e., where diffusivity is greaterthan 500 μm²/hr or may be characterized as greater than 450 μm²/hour at460° C.

At a certain temperature the diffusivity is calculated using theequation (4):Diffusivity=DOL^2/5.6*T  (4)in which DOL is depth of ion-exchange layer and T is the IOX time ittakes to reach that DOL.

The glass-based article may include an amorphous substrate, acrystalline substrate or a combination thereof (e.g., a glass-ceramicsubstrate). In one or more embodiments, the glass-based articlesubstrate (prior to being chemically strengthened as described herein)may include a glass having a composition, in mole percent (mole %),including:

SiO₂ in the range from about 40 to about 80, Al₂O₃ in the range fromabout 10 to about 30, B₂O₃ in the range from about 0 to about 10, R₂O inthe range from about 0 to about 20, and RO in the range from about 0 toabout 15. In some instances, the composition may include either one orboth of ZrO₂ in the range from about 0 mol % to about 5 mol % and P₂O₅in the range from about 0 to about 15 mol %. TiO2 can be present fromabout 0 mol % to about 2 mol %.

In some embodiments, the glass composition may include SiO₂ in anamount, in mol %, in the range from about 45 to about 80, from about 45to about 75, from about 45 to about 70, from about 45 to about 65, fromabout 45 to about 60, from about 45 to about 65, from about 45 to about65, from about 50 to about 70, from about 55 to about 70, from about 60to about 70, from about 70 to about 75, from about 70 to about 72, orfrom about 50 to about 65.

In some embodiments, the glass composition may include Al₂O₃ in anamount, in mol %, in the range from about 5 to about 28, from about 5 toabout 26, from about 5 to about 25, from about 5 to about 24, from about5 to about 22, from about 5 to about 20, from about 6 to about 30, fromabout 8 to about 30, from about 10 to about 30, from about 12 to about30, from about 14 to about 30, from about 16 to about 30, from about 18to about 30, from about 18 to about 28, or from about 12 to about 15.

In one or more embodiments, the glass composition may include B₂O₃ in anamount, in mol %, in the range from about 0 to about 8, from about 0 toabout 6, from about 0 to about 4, from about 0.1 to about 8, from about0.1 to about 6, from about 0.1 to about 4, from about 1 to about 10,from about 2 to about 10, from about 4 to about 10, from about 2 toabout 8, from about 0.1 to about 5, or from about 1 to about 3. In someinstances, the glass composition may be substantially free of B₂O₃. Asused herein, the phrase “substantially free” with respect to thecomponents of the glass composition means that the component is notactively or intentionally added to the glass compositions during initialbatching or subsequent ion exchange, but may be present as an impurity.For example, a glass may be describe as being substantially free of acomponent, when the component is present in an amount of less than about0.1001 mol %.

In some embodiments, the glass composition may include one or morealkali earth metal oxides, such as MgO, CaO and ZnO. In someembodiments, the total amount of the one or more alkali earth metaloxides may be a non-zero amount up to about 15 mol %. In one or morespecific embodiments, the total amount of any of the alkali earth metaloxides may be a non-zero amount up to about 14 mol %, up to about 12 mol%, up to about 10 mol %, up to about 8 mol %, up to about 6 mol %, up toabout 4 mol %, up to about 2 mol %, or up about 1.5 mol %. In someembodiments, the total amount, in mol %, of the one or more alkali earthmetal oxides may be in the range from about 0.1 to 10, from about 0.1 to8, from about 0.1 to 6, from about 0.1 to 5, from about 1 to 10, fromabout 2 to 10, or from about 2.5 to 8. The amount of MgO may be in therange from about 0 mol % to about 5 mol % (e.g., from about 2 mol % toabout 4 mol %). The amount of ZnO may be in the range from about 0 toabout 2 mol %. The amount of CaO may be from about 0 mol % to about 2mol %. In one or more embodiments, the glass composition may include MgOand may be substantially free of CaO and ZnO. In one variant, the glasscomposition may include any one of CaO or ZnO and may be substantiallyfree of the others of MgO, CaO and ZnO. In one or more specificembodiments, the glass composition may include only two of the alkaliearth metal oxides of MgO, CaO and ZnO and may be substantially free ofthe third of the earth metal oxides.

The total amount, in mol %, of alkali metal oxides R₂O in the glasscomposition may be in the range from about 5 to about 20, from about 5to about 18, from about 5 to about 16, from about 5 to about 15, fromabout 5 to about 14, from about 5 to about 12, from about 5 to about 10,from about 5 to about 8, from about 5 to about 20, from about 6 to about20, from about 7 to about 20, from about 8 to about 20, from about 9 toabout 20, from about 10 to about 20, from about 6 to about 13, or fromabout 8 to about 12.

In one or more embodiments, the glass composition includes Na₂O in anamount in the range from about 0 mol % to about 18 mol %, from about 0mol % to about 16 mol % or from about 0 mol % to about 14 mol %, fromabout 0 mol % to about 10 mol %, from about 0 mol % to about 5 mol %,from about 0 mol % to about 2 mol %, from about 0.1 mol % to about 6 mol%, from about 0.1 mol % to about 5 mol %, from about 1 mol % to about 5mol %, from about 2 mol % to about 5 mol %, or from about 10 mol % toabout 20 mol %.

In some embodiments, the amount of Li₂O and Na₂O is controlled to aspecific amount or ratio to balance formability and ion exchangeability.For example, as the amount of Li₂O increases, the liquidus viscosity maybe reduced, thus preventing some forming methods from being used;however, such glass compositions are ion exchanged to deeper DOC levels,as described herein. The amount of Na₂O can modify liquidus viscositybut can inhibit ion exchange to deeper DOC levels.

In one or more embodiments, the glass composition may include K₂O in anamount less than about 5 mol %, less than about 4 mol %, less than about3 mol %, less than about 2 mol %, or less than about 1 mol %. In one ormore alternative embodiments, the glass composition may be substantiallyfree, as defined herein, of K₂O.

In one or more embodiments, the glass composition may include Li₂O in anamount about 0 mol % to about 18 mol %, from about 0 mol % to about 15mol % or from about 0 mol % to about 10 mol %, from about 0 mol % toabout 8 mol %, from about 0 mol % to about 6 mol %, from about 0 mol %to about 4 mol % or from about 0 mol % to about 2 mol %. In someembodiments, the glass composition may include Li₂O in an amount about 2mol % to about 10 mol %, from about 4 mol % to about 10 mol %, fromabout 6 mol % to about 10 mol, or from about 5 mol % to about 8 mol %.In one or more alternative embodiments, the glass composition may besubstantially free, as defined herein, of Li₂O.

In one or more embodiments, the glass composition may include Fe₂O₃. Insuch embodiments, Fe₂O₃ may be present in an amount less than about 1mol %, less than about 0.9 mol %, less than about 0.8 mol %, less thanabout 0.7 mol %, less than about 0.6 mol %, less than about 0.5 mol %,less than about 0.4 mol %, less than about 0.3 mol %, less than about0.2 mol %, less than about 0.1 mol % and all ranges and sub-rangestherebetween. In one or more alternative embodiments, the glasscomposition may be substantially free, as defined herein, of Fe₂O₃.

In one or more embodiments, the glass composition may include ZrO₂. Insuch embodiments, ZrO₂ may be present in an amount less than about 1 mol%, less than about 0.9 mol %, less than about 0.8 mol %, less than about0.7 mol %, less than about 0.6 mol %, less than about 0.5 mol %, lessthan about 0.4 mol %, less than about 0.3 mol %, less than about 0.2 mol%, less than about 0.1 mol % and all ranges and sub-ranges therebetween.In one or more alternative embodiments, the glass composition may besubstantially free, as defined herein, of ZrO₂.

In one or more embodiments, the glass composition may include P₂O₅ in arange from about 0 mol % to about 10 mol %, from about 0 mol % to about8 mol %, from about 0 mol % to about 6 mol %, from about 0 mol % toabout 4 mol %, from about 0.1 mol % to about 10 mol %, from about 0.1mol % to about 8 mol %, from about 4 mol % to about 8 mol %, or fromabout 5 mol % to about 8 mol %. In some instances, the glass compositionmay be substantially free of P₂O₅.

In one or more embodiments, the glass composition may include TiO₂. Insuch embodiments, TiO₂ may be present in an amount less than about 6 mol%, less than about 4 mol %, less than about 2 mol %, or less than about1 mol %. In one or more alternative embodiments, the glass compositionmay be substantially free, as defined herein, of TiO₂. In someembodiments, TiO₂ is present in an amount in the range from about 0.1mol % to about 6 mol %, or from about 0.1 mol % to about 4 mol %.

In some embodiments, the glass composition may include variouscompositional relationships. For example, the glass composition mayinclude a ratio of the amount of Li₂O (in mol %) to the total amount ofR₂O (in mol %) in the range from about 0.5 to about 1. In someembodiments, the glass composition may include a difference between thetotal amount of R₂O (in mol %) to the amount of Al₂O₃ (in mol %) in therange from about −5 to about 0. In some instances the glass compositionmay include a difference between the total amount of R_(x)O (in mol %)and the amount of Al₂O₃ in the range from about 0 to about 3. The glasscomposition of one or more embodiments may exhibit a ratio of the amountof MgO (in mol %) to the total amount of RO (in mol %) in the range fromabout 0 to about 2.

In some embodiments, glass composition may be substantially free ofnucleating agents. Examples of typical nucleating agents are TiO₂, ZrO₂and the like. Nucleating agents may be described in terms of function inthat nucleating agents are constituents in the glass can initiate theformation of crystallites in the glass.

In some embodiments, the compositions used for the glass substrate maybe batched with 0-2 mol % of at least one fining agent selected from agroup that includes Na₂SO₄, NaCl, NaF, NaBr, K₂SO₄, KCl, KF, KBr, andSnO₂. The glass composition according to one or more embodiments mayfurther include SnO₂ in the range from about 0 to about 2, from about 0to about 1, from about 0.1 to about 2, from about 0.1 to about 1, orfrom about 1 to about 2. The glass compositions disclosed herein may besubstantially free of As₂O₃ and/or Sb₂O₃.

In one or more embodiments, the composition may specifically include 62mol % to 75 mol % SiO₂; 10.5 mol % to about 17 mol % Al₂O₃; 5 mol % toabout 13 mol % Li₂O; 0 mol % to about 4 mol % ZnO; 0 mol % to about 8mol % MgO; 2 mol % to about 5 mol % TiO₂; 0 mol % to about 4 mol % B₂O₃;0 mol % to about 5 mol % Na₂O; 0 mol % to about 4 mol % K₂O; 0 mol % toabout 2 mol % ZrO₂; 0 mol % to about 7 mol % P₂O₅; 0 mol % to about 0.3mol % Fe₂O₃; 0 mol % to about 2 mol % MnOx; and 0.05 mol % to about 0.2mol % SnO₂. In one or more embodiments, the composition may include 67mol % to about 74 mol % SiO₂; 11 mol % to about 15 mol % Al₂O₃; 5.5 mol% to about 9 mol % Li₂O; 0.5 mol % to about 2 mol % ZnO; 2 mol % toabout 4.5 mol % MgO; 3 mol % to about 4.5 mol % TiO₂; 0 mol % to about2.2 mol % B₂O₃; 0 mol % to about 1 mol % Na₂O; 0 mol % to about 1 mol %K₂O; 0 mol % to about 1 mol % ZrO₂; 0 mol % to about 4 mol % P₂O₅; 0 mol% to about 0.1 mol % Fe₂O₃; 0 mol % to about 1.5 mol % MnOx; and 0.08mol % to about 0.16 mol % SnO₂. In one or more embodiments, thecomposition may include 70 mol % to 75 mol % SiO₂; 10 mol % to about 15mol % Al₂O₃; 5 mol % to about 13 mol % Li₂O; 0 mol % to about 4 mol %ZnO; 0.1 mol % to about 8 mol % MgO; 0 mol % to about 5 mol % TiO₂, 0.1mol % to about 4 mol % B₂O₃; 0.1 mol % to about 5 mol % Na₂O; 0 mol % toabout 4 mol % K₂O; 0 mol % to about 2 mol % ZrO₂; 0 mol % to about 7 mol% P₂O₅; 0 mol % to about 0.3 mol % Fe₂O₃; 0 mol % to about 2 mol % MnOx;and 0.05 mol % to about 0.2 mol % SnO₂.

In one or more embodiments, the composition may include 52 mol % toabout 63 mol % SiO₂; 11 mol % to about 15 mol % Al₂O₃; 5.5 mol % toabout 9 mol % Li₂O; 0.5 mol % to about 2 mol % ZnO; 2 mol % to about 4.5mol % MgO; 3 mol % to about 4.5 mol % TiO₂; 0 mol % to about 2.2 mol %B₂O₃; 0 mol % to about 1 mol % Na₂O; 0 mol % to about 1 mol % K₂O; 0 mol% to about 1 mol % ZrO₂; 0 mol % to about 4 mol % P₂O₅; 0 mol % to about0.1 mol % Fe₂O₃; 0 mol % to about 1.5 mol % MnOx; and 0.08 mol % toabout 0.16 mol % SnO₂.

Other exemplary compositions of glass-based articles prior to beingchemically strengthened, as described herein, are shown in Table 1.

TABLE 1 Exemplary compositions prior to chemical strengthening. Mol %Ex. A Ex. B Ex. C Ex. D Ex. E Ex. F SiO₂ 71.8 69.8 69.8 69.8 69.8 69.8Al₂O₃ 13.1 13 13 13 13 13 B₂O₃ 2 2.5 4 2.5 2.5 4 Li₂O 8 8.5 8 8.5 8.5 8MgO 3 3.5 3 3.5 1.5 1.5 ZnO 1.8 2.3 1.8 2.3 2.3 1.8 Na₂O 0.4 0.4 0.4 0.40.4 0.4 TiO₂ 0 0 0 1 1 1 Fe₂O₃ 0 0 0 0.8 0.8 0.8 SnO₂ 0.1 0.1 0.1 0.10.1 0.1 Mol % Ex. G Ex. H Ex. I Ex. J Ex. K Ex. L Ex. M Ex. N SiO₂ 70.1870.91 71.28 71.65 71.65 71.65 74.77 72.00 Al₂O₃ 12.50 12.78 12.93 13.0713.07 13.07 10.00 12.50 B₂O₃ 1.91 1.95 1.98 2.00 2.00 2.00 1.99 2.00Li₂O 7.91 7.95 7.96 7.98 6.98 5.00 6.13 6.00 Na₂O 4.43 2.43 1.42 0.411.41 3.40 3.97 0.50 MgO 2.97 2.98 2.99 3.00 3.00 3.00 2.94 2.10 ZnO 0.000.89 1.34 1.80 1.80 1.80 0.00 0.00 CaO 0.00 0.00 0.00 0.00 0.00 0.000.05 4.90 SnO₂ 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 Li₂O/R₂O 0.640.77 0.85 0.95 0.83 0.60 0.61 0.92 R₂O − −0.16 −2.41 −3.54 −4.68 −4.68−4.67 0.10 −6.00 Al₂O₃ R_(x)O − 2.81 1.47 0.79 0.12 0.12 0.13 3.09 1.00Al₂O₃ MgO/RO 1.00 0.77 0.69 0.63 0.63 0.63 1.00 1.00 R₂O 12.34 10.389.39 8.39 8.39 8.40 10.10 6.50 RO 2.97 3.88 4.34 4.79 4.79 4.79 2.997.00

Where the glass-based article includes a glass-ceramic, the crystalphases may include β-spodumene, rutile, gahnite or other known crystalphases and combinations thereof.

The glass-based article may be substantially planar, although otherembodiments may utilize a curved or otherwise shaped or sculptedsubstrate. In some instances, the glass-based article may have a 3D or2.5D shape. The glass-based article may be substantially opticallyclear, transparent and free from light scattering. The glass-basedarticle may have a refractive index in the range from about 1.45 toabout 1.55. As used herein, the refractive index values are with respectto a wavelength of 550 nm.

Additionally or alternatively, the thickness of the glass-based articlemay be constant along one or more dimension or may vary along one ormore of its dimensions for aesthetic and/or functional reasons. Forexample, the edges of the glass-based article may be thicker as comparedto more central regions of the glass-based article. The length, widthand thickness dimensions of the glass-based article may also varyaccording to the article application or use.

The glass-based article may be characterized by the manner in which itis formed. For instance, where the glass-based article may becharacterized as float-formable (i.e., formed by a float process),down-drawable and, in particular, fusion-formable or slot-drawable(i.e., formed by a down draw process such as a fusion draw process or aslot draw process).

A float-formable glass-based article may be characterized by smoothsurfaces and uniform thickness is made by floating molten glass on a bedof molten metal, typically tin. In an example process, molten glass thatis fed onto the surface of the molten tin bed forms a floating glassribbon. As the glass ribbon flows along the tin bath, the temperature isgradually decreased until the glass ribbon solidifies into a solidglass-based article that can be lifted from the tin onto rollers. Onceoff the bath, the glass glass-based article can be cooled further andannealed to reduce internal stress. Where the glass-based article is aglass ceramic, the glass-based article formed from the float process maybe subjected to a ceramming process by which one or more crystallinephases are generated.

Down-draw processes produce glass-based articles having a uniformthickness that possess relatively pristine surfaces. Because the averageflexural strength of the glass-based article is controlled by the amountand size of surface flaws, a pristine surface that has had minimalcontact has a higher initial strength. When this high strengthglass-based article is then further strengthened (e.g., chemically), theresultant strength can be higher than that of a glass-based article witha surface that has been lapped and polished. Down-drawn glass-basedarticles may be drawn to a thickness of less than about 2 mm. Inaddition, down drawn glass-based articles have a very flat, smoothsurface that can be used in its final application without costlygrinding and polishing. Where the glass-based article is a glassceramic, the glass-based article formed from the down draw process maybe subjected to a ceramming process by which one or more crystallinephases are generated.

The fusion draw process, for example, uses a drawing tank that has achannel for accepting molten glass raw material. The channel has weirsthat are open at the top along the length of the channel on both sidesof the channel. When the channel fills with molten material, the moltenglass overflows the weirs. Due to gravity, the molten glass flows downthe outside surfaces of the drawing tank as two flowing glass films.These outside surfaces of the drawing tank extend down and inwardly sothat they join at an edge below the drawing tank. The two flowing glassfilms join at this edge to fuse and form a single flowing glass-basedarticle. The fusion draw method offers the advantage that, because thetwo glass films flowing over the channel fuse together, neither of theoutside surfaces of the resulting glass-based article comes in contactwith any part of the apparatus. Thus, the surface properties of thefusion drawn glass-based article are not affected by such contact. Wherethe glass-based article is a glass ceramic, the glass-based articleformed from the fusion process may be subjected to a ceramming processby which one or more crystalline phases are generated.

The slot draw process is distinct from the fusion draw method. In slowdraw processes, the molten raw material glass is provided to a drawingtank. The bottom of the drawing tank has an open slot with a nozzle thatextends the length of the slot. The molten glass flows through theslot/nozzle and is drawn downward as a continuous glass-based articleand into an annealing region. Where the glass-based article is a glassceramic, the glass-based article formed from the slot draw process maybe subjected to a ceramming process by which one or more crystallinephases are generated.

In some embodiments, the glass-based article may be formed using a thinrolling process, as described in U.S. Pat. No. 8,713,972, entitled“Precision Glass Roll Forming Process and Apparatus”, U.S. Pat. No.9,003,835, entitled “Precision Roll Forming of Textured Sheet Glass”,U.S. Patent Publication No. 20150027169, entitled “Methods And ApparatusFor Forming A Glass Ribbon”, and U.S. Patent Publication No.20050099618, entitled “Apparatus and Method for Forming Thin GlassArticles”, the contents of which are incorporated herein by reference intheir entirety. More specifically the glass-based article may be formedby supplying a vertical stream of molten glass, forming the suppliedstream of molten glass or glass-ceramic with a pair of forming rollsmaintained at a surface temperature of about 500° C. or higher or about600° C. or higher to form a formed glass ribbon having a formedthickness, sizing the formed ribbon of glass with a pair of sizing rollsmaintained at a surface temperature of about 400° C. or lower to producea sized glass ribbon having a desired thickness less than the formedthickness and a desired thickness uniformity. The apparatus used to formthe glass ribbon may include a glass feed device for supplying asupplied stream of molten glass; a pair of forming rolls maintained at asurface temperature of about 500° C. or higher, the forming rolls beingspaced closely adjacent each other defining a glass forming gap betweenthe forming rolls with the glass forming gap located vertically belowthe glass feed device for receiving the supplied stream of molten glassand thinning the supplied stream of molten glass between the formingrolls to form a formed glass ribbon having a formed thickness; and apair of sizing rolls maintained at a surface temperature of about 400°C. or lower, the sizing rolls being spaced closely adjacent each otherdefining a glass sizing gap between the sizing rolls with the glasssizing gap located vertically below the forming rolls for receiving theformed glass ribbon and thinning the formed glass ribbon to produce asized glass ribbon having a desired thickness and a desired thicknessuniformity.

In some instances, the thin rolling process may be utilized where theviscosity of the glass does not permit use of fusion or slot drawmethods. For example, thin rolling can be utilized to form theglass-based articles when the glass exhibits a liquidus viscosity lessthan 100 kP.

The glass-based article may be acid polished or otherwise treated toremove or reduce the effect of surface flaws.

Another aspect of this disclosure pertains to a method of forming afracture-resistant glass-based article. The method includes providing aglass-based substrate having a first surface and a second surfacedefining a thickness of about 1 millimeter or less and generating astress profile in the glass-based substrate, as described herein toprovide the fracture-resistant glass-based article. In one or moreembodiments, generating the stress profile comprises ion exchanging aplurality of alkali ions into the glass-based substrate to form anon-zero alkali metal oxide concentration that varies along asubstantial portion of the thickness (as described herein) or along theentire thickness. In one example, generating the stress profile includesimmersing the glass-based substrate in a molten salt bath includingnitrates of Na+, K+, Rb+, Cs+ or a combination thereof, having atemperature of about 350° C. or greater (e.g., about 350° C. to about500° C.). In one example, the molten bath may include NaNO₃ and may havea temperature of about 485° C. In another example, the bath may includeNaNO₃ and have a temperature of about 430° C. The glass-based substratemay be immersed in the bath for about 2 hours or more, up to about 48hours (e.g., from about 12 hours to about 48 hours, from about 12 hoursto about 32 hours, from about 16 hours to about 32 hours, from about 16hours to about 24 hours, or from about 24 hours to about 32 hours).

In some embodiments, the method may include chemically strengthening orion exchanging the glass-based substrate in more than one step usingsuccessive immersion steps in more than one bath. For example, two ormore baths may be used successively. The composition of the one or morebaths may include a single metal (e.g., Ag+, Na+, K+, Rb+, or Cs+) or acombination of metals in the same bath. When more than one bath isutilized, the baths may have the same or different composition and/ortemperature as one another. The immersion times in each such bath may bethe same or may vary to provide the desired stress profile.

In one or more embodiments, a second bath or subsequent baths may beutilized to generate a greater surface CS. In some instances, the methodincludes immersing the glass-based substrate in the second or subsequentbaths to generate a greater surface CS, without significantlyinfluencing the chemical depth of layer and/or the DOC. In suchembodiments, the second or subsequent bath may include a single metal(e.g., KNO₃ or NaNO₃) or a mixture of metals (KNO₃ and NaNO₃). Thetemperature of the second or subsequent bath may be tailored to generatethe greater surface CS. In some embodiments, the immersion time of theglass-based substrate in the second or subsequent bath may also betailored to generate a greater surface CS without influencing thechemical depth of layer and/or the DOC. For example, the immersion timein the second or subsequent baths may be less than 10 hours (e.g., about8 hours or less, about 5 hours or less, about 4 hours or less, about 2hours or less, about 1 hour or less, about 30 minutes or less, about 15minutes or less, or about 10 minutes or less).

In one or more alternative embodiments, the method may include one ormore heat treatment steps which may be used in combination with theion-exchanging processes described herein. The heat treatment includesheat treating the glass-based article to obtain a desired stressprofile. In some embodiments, heat treating includes annealing,tempering or heating the glass-based substrate to a temperature in therange from about 300° C. to about 600° C. The heat treatment may lastfor 1 minute up to about 18 hours. In some embodiments, the heattreatment may be used after one or more ion-exchanging processes, orbetween ion-exchanging processes.

EXAMPLES

Various embodiments will be further clarified by the following examples.In the Examples, prior to being strengthened, the Examples are referredto as “substrates”. After being subjected to strengthening, the Examplesare referred to as “articles” or “glass-based articles”.

Example 1

Glass-ceramic substrates having a nominal composition as shown below inTable 2 was provided. The glass-ceramic substrates had a thickness of0.8 millimeters and included a crystal phase assemblage comprising aβ-spodumene solid solution as a predominant crystalline phase and one ormore minor phases including rutile. The glass-ceramic substrates wereimmersed in a molten salt bath including NaNO₃ having a temperature of485° C. for 10 hours (Condition A), 13 hours (Condition B) or 24 hours(Condition C), or a molten salt bath including NaNO₃ having atemperature of 430° C. for the 2 hours (Comparative Condition D) to formglass-ceramic articles.

TABLE 2 Composition of the glass-ceramic substrate of Example 1, priorto chemical strengthening. Example = 

Oxide [mole %] 1 SiO₂ 69.2 Al₂O₃ 12.6 B₂O₃  1.8 Li₂O  7.7 Na₂O  0.4 MgO 2.9 ZnO  1.7 TiO₂  3.5 SnO₂  0.1$\frac{\left\lbrack {{{Li}_{2}O} + {{Na}_{2}O} + {MgO} + {ZnO} + {K_{2}O}} \right\rbrack}{\left\lbrack {{{Al}_{2}O_{3}} + {B_{2}O_{3}}} \right\rbrack}$$\frac{12.7}{14.4} = 0.88$$\frac{\left\lbrack {{TiO}_{2} + {SnO}_{2}} \right\rbrack}{\left\lbrack {{SiO}_{2} + {B_{2}O_{3}}} \right\rbrack}$$\frac{3.6}{71} = 0.051$

The stress profiles of the glass-ceramic articles were measured bymicroprobe and are shown in FIG. 5. As shown in FIG. 5, the Na+ ions areion exchanged through almost the entire thickness of the articles when ahigher temperature bath is utilized (i.e., Conditions A-C). In suchglass-ceramics, Na₂O is present in the CT region in an amount of about1.2 mol % or greater. The glass-ceramic article ion exchanged in a lowertemperature bath (Comparative Condition D) exhibited a stress profilethat resembles known stress profiles.

Example 2

Glass substrates having the same composition as shown in Table 2 and athickness of 0.8 mm, but having an amorphous structure (and no crystalphases) were chemically strengthened by immersing in a molten salt bathincluding 100% NaNO₃ having a temperature of about 430° C. for variousdurations to provide glass articles. The DO) and the maximum CT value ofthe glass articles were measured using a scattered light polariscope(SCALP). As shown in FIG. 6, the DOC and the maximum CT increases withincreased length of immersion or ion exchange. The greatest CT valueswere observed after immersing the glasses for about 16 hours.

The stress profiles of the glass articles of Example 2 were measuredusing SCALP and are shown in FIG. 7. The upper portion of the x-axisindicating a positive stress value is the CT layer and the lower portionof the x-axis indicating a negative stress value is the CS values. Thestress profile of the glass article that was chemically strengthened for16 hours exhibited the greatest CT value (i.e., 175 MPa) and a shapethat was parabolic-like, which included substantially no linearportions, in a depth direction, of 100 micrometers. The surface CSmeasured by SCALP was about 410 MPa. Accordingly, the ratio of maximumCT to surface CS of Example 2 is about 0.4375.

Example 3

For comparison, the glass-ceramic substrate of Example 1 and the glasssubstrate of Example 2, each having a thickness of about 0.8 mm, weresubjected to chemical strengthening by immersing in a molten salt bathof NaNO₃ having a temperature of 350° C. for 3.5 hours (Example 3A and3B, respectively). The resulting stress profiles of the glass-ceramicarticle and glass article shown in FIG. 8 resemble an error function(erfc) or quasi-linear shape. Moreover, the CS depth of layer is lessthan the depth of the alkali ion exchanged into the glass orglass-ceramic (or the chemical ion exchange depth).

When the glass-ceramic substrate of Example 1 and the glass substrate ofExample 2, each having a thickness of about 0.8 mm were subjected to thechemical strengthening described herein by immersing in a molten saltbath of NaNO₃ having a temperature of 430° C. for 24 hours (Examples 3Cand 3D, respectively), the resulting glass-based articles exhibitedmetal oxide concentration profiles (obtained by EPMA) as shown in FIG.9. The metal oxide concentration profiles are parabolic-like and show aion exchange of Na+ ions throughout the entire thickness. The chemicalprofiles were measured using EMPA and the chemical depth of Na₂Odiffusion is shown as equal to or larger than 400 micrometers. Moreover,Na₂O is present in a concentration of about 1 mol % or greaterthroughout the thickness, including in the CT layer. The resultingglass-ceramic articles of Example 3D exhibited superior fractureresistance in a drop test in which the glass-ceramic substrates wereretrofitted into an identical mobile phone housing. Specifically, Fivesamples of Example 3D were assembled in a mobile phone device anddropped onto sandpaper for successive drops starting at a height of 50cm. As each sample survived the drop from a height, it was dropped againfrom an increase height until it fractured, at which point the failureheight of that sample was recorded in FIG. 9A. Example 3D exhibited anaverage failure height of 172.5 cm.

FIG. 10 shows stress profiles of a glass-based substrate chemicallystrengthened according to known processes and a glass-based substratechemically strengthened according to the methods described herein. Asshown in FIG. 10, the stress profile of the glass-based articles of theembodiments described herein have a shape that is substantially free oflinear segments (having a length or absolute depth greater than about 50micrometers) and exhibits a DOC of about 0.2·t, while the known stressprofile exhibits a substantially linear portion from a depth of about0.1 millimeters to about 0.7 millimeters (for a total length of about0.6 millimeters or 600 micrometers). The known stress profile alsoexhibits a lower CT value and a lower DOC.

Example 4

Glass substrates (each having a thickness of about 1 mm) having thecomposition of Table 2 were subjected to chemical strengthening byimmersing in a first molten salt bath of NaNO₃ having a temperature of430° C. for 24 hours. One glass-based article was not subjected to anyadditional strengthening steps (Example 4A). Three glass-based articleswere subjected to a second strengthening step by immersion in a secondmolten salt bath of KNO₃ having a temperature of about 430° C. foreither 0.75 hours, 4 hours, or 8 hours (Examples 4B, 4C and 4D,respectively). The stress profiles as measured by SCALP of the resultingglass-based articles are shown in FIG. 11, with depth or thickness ofthe glass-based articles plotted on the x-axis and stress plotted on they-axis. The positive stress values are CT values and the negative stressvalues are the CS values. Spatial resolution of the instrument prohibitsmeasurement of the CS associated with the second KNO₃ ion exchange step.The glass-based articles of Examples 4A and 4B exhibited similarprofiles. The glass-based articles of Examples 4C and 4D exhibiteddecreasing CT (as compared to Examples 4A and 4B) and decreasing CS (ascompared to Examples 4A and 4B), with time and after the immersion atsecond strengthening step. The glass-based articles of Examples 4C and4D also exhibited increased DOC, as compared to Examples 4A and 4B, andsuch DOC values were greater than 0.2·t.

FIG. 12 shows the stored tensile energy in J/m² for each of Examples4B-4D, which are greater than 15 J/m² depending on time immersed in thesecond molten salt bath of KNO₃. The stored tensile energy can becalculated from the measured SCALP stress profile data and usingequation (3) above.

FIGS. 13 and 14 show the concentration profiles of each of K₂O and Na₂Oas a function of depth (in micrometers) each of Examples 4B-4D. As shownin FIG. 13, the chemical depth of K₂O is 3 micrometers (Ex. 4B,immersion for 0.75 hours in a KNO₃ bath), 6 micrometers (Ex. 4C,immersion for 4 hours in a KNO₃ bath) and 5 micrometers (Ex. 4D,immersion for 8 hours in a KNO₃ bath). As shown in FIG. 14, Na₂Openetrates the entire depth and has a concentration of about 1 mol % orgreater for each of Examples 4B-4D along the entire depth of theglass-based article.

Examples 4E and 4F included glass substrates (each having a thickness ofabout 1 mm) having the composition of Table 2, which were subjected tochemical strengthening by immersing in a first molten salt bath of NaNO₃having a temperature of 430° C. for 24 hours, followed by heat treatmentto a temperature of 430° C. in air for 4 hours or 8.25 hours,respectively. The stress profiles of the glass-based articles ofExamples 4E, 4F are shown in FIG. 15, with the stress profiles forExamples 4A, 4C and 4D shown for comparison. FIG. 16 shows the samegraph as FIG. 15, at a smaller scale to illustrate the differences inthe stress profiles at or near a depth of 0.5·t.

Example 5

Glass substrates (each having a thickness of about 1 mm) having thecomposition of Table 2 were subjected to chemical strengthening byimmersing in a first molten salt bath of NaNO₃ having a temperature of430° C. for 24 hours. One glass-based article was not subjected to anyadditional strengthening steps (Example 5A). Two glass-based articleswere subjected to a second strengthening step by placing the glass-basedarticles in a furnace at 390° C. and maintaining the glass-basedarticles in the furnace for about 8 hours or 28 hours (Examples 5B-5C,respectively). Four glass-based articles were subjected to a thirdstrengthening step (after the first strengthening step and either of thedifferent second strengthening steps) by immersing in a second moltensalt bath of KNO3 having a temperature of 430° C. for 4 hours or 8 hours(Examples 5D-5G). The strengthening steps for each of Examples 5A-5G isshown in Table 3. The measured CT values are also shown in Table 3.

TABLE 3 Strengthening steps for Examples 5A-5G. Step Ex. 5A Ex. 5B Ex.5C Ex. 5D Ex. 5E Ex. 5F Ex. 5G 1^(st) Step NaNO₃, NaNO₃, NaNO₃, NaNO₃,NaNO₃, NaNO₃, NaNO₃, 430° C., 430° C., 430° C., 430° C., 430° C., 430°C., 430° C., 24 hours 24 hours 24 hours 24 hours 24 hours 24 hours 24hours 2^(nd) Step Air, 390° C., 8 Air, 390° C., Air, 390° C., 8 Air,390° C., Air, 390° C., 8 Air, 390° C., hours 28 hours 28 hours 28 hourshours hours 3^(rd) Step KNO₃, KNO₃, KNO₃, KNO₃, 430° C., 4 430° C., 4430° C., 8 430° C., 8 hours hours hours hours CT 174 MPa 148 MPa 96 MPa129 MPa 82 MPa 103 MPa 72 MPa

The stress profiles of the resulting glass-based articles are shown inFIG. 17, with depth or thickness of the glass-based articles plotted onthe x-axis and stress plotted on the y-axis. The positive stress valuesare CT values and the negative stress values are the CS values. As shownin FIG. 17, as the duration of the second and/or third heat treatmentsis increased, the DOC increased and the CT decreased. The decrease inDOC and CT in shown more clearly in FIGS. 18 and 19, respectively.

The glass-based articles of Examples 5A-5G were then subjected to a poketest in which one side of the glass-based article is adhered to tape andthe opposite bare side is impacted with sharp implement and fractured.The resulting number of fragments can be correlated to the storedtensile energy of the glass-based article. Examples 5A, 5B and 5Dexhibited numerous fragments (i.e, in excess of 50 and even 100), whileExample 5F exhibited 10 fragments, Example 5C exhibited 3 fragments, andExample 5E and 5G exhibited 4 fragments. Examples 5A, 5B and 5D, whichfractured into numerous fragments exhibited higher CT (greater thanabout 100 MPa) than Examples 5C, 5E, 5F and 5G which all had CT valuesof about 100 MPa or less.

Example 6

Glass substrates having a nominal composition of 57.5 mol % SiO₂, 16.5mol % Al₂O₃, 16.7 mol % Na₂O, 2.5 mol % MgO, and 6.5 mol % P₂O₅, andhaving a thicknesses of about 0.4 mm, 0.55 mm, or 1 mm were subjected tochemical strengthening. The thicknesses and conditions of chemicalstrengthening are shown in Table 4.

TABLE 4 Thickness and chemical strengthening conditions for Examples6A-6D. Bath Ex. Thickness Bath Composition Temperature 6A  0.4 mm 80%KNO3, 20% NaNO3 430° C. 6B 0.55 mm 80% KNO₃, 20% NaNO₃ 430° C. 6C 0.55mm 90% KNO₃, 10% NaNO₃ 430° C. 6D  1.0 mm 70% KNO₃, 30% NaNO₃ 430° C.

Example 6A was immersed in a molten salt bath, as indicted in Table 4,for 4 hours, 8 hours, 16 hours, 32 hours, 64 hours and 128 hours(Examples 6A-1 through 6A-6). Example 6B was immersed in a molten saltbath, as indicated in Table 4, for 4 hours, 8 hours, 16 hours, 32 hours,64 hours and 128 hours (Examples 6B-1 through 6B-6). Example 6C wasimmersed in a molten salt bath, as indicated in Table 4, for 1 hour, 2hours, 4 hours, 8 hours, 16 hours and 32 hours (Examples 6C-1 through6C-6). Example 6D was immersed in a molten salt bath, as indicated inTable 4, for 4 hours, 8 hours, 16 hours, 32 hours, 64 hours and 128hours (Examples 6D-1 through 6D-6). The stress profiles of Examples 6A-1through 6A-6, 6B-1 through 6B-6, 6C-1 through 6C-6, and 6D-1 through6D-6 are shown in FIGS. 20, 22, 24 and 26, respectively. In FIGS. 20,22, 24 and 26, the depth or thickness of the glass articles is plottedon the x-axis and stress is plotted on the y-axis. The positive stressvalues are CT values and the negative stress values are the CS values.

The CT and DOC values as a function of time immersed in the molten saltbath for Examples 6A-1 through 6A-6, Examples 6B-1 through 6B-6,Examples 6C-1 through 6C-6 and 6D-1 through 6D-6, are shown in FIGS. 21,23, 25, and 27, respectively.

Example 7

Glass substrates having a nominal composition as shown in Table 2 andhaving a thicknesses of about 1 mm were subjected to chemicalstrengthening in a molten salt bath including 100% NaNO₃ and atemperature of 430° C. The duration for which the glass substrates wereimmersed in the molten salt bath are shown in Table 5.

TABLE 4 Chemical strengthening duration (or ion exchange times) forExamples 7A-7G. Ex. IOX Time (hours) 7A 2 7B 4 7C 8 7D 16 7E 24 7F 32.57G 48

The stress profiles of the glass-based articles of Examples 7A-7G areshown in FIG. 28. The stress profiles were measured using SCALP. Asshown in FIG. 28, immersion of the glass substrates in the molten saltbath for 16 hours and 24 hours results in glass-based articlesexhibiting the greatest surface CS values and the greatest CT values, inabsolute terms. A graph showing the change in CT values and storedtensile energy, both as a function of ion exchange time is shown in FIG.29.

Example 8

Glass substrates having a nominal composition as shown in Table 2 andhaving a thicknesses of about 0.8 mm each were subjected to chemicalstrengthening in a molten salt bath including a mixture of NaNO₃ andNaSO₄ and a temperature of 500° C. for 15 minutes (Comparative Example8A) and for 16 hours (Example 8B). The stress profile of the glass-basedarticles of Examples 8A and 8B are shown in FIG. 30. A shown in FIG. 30,Comparative Example 8A exhibited a known stress profile, whereas,Example 8B showed a stress profile according to one or more embodimentsof this disclosure. The stored tensile energy of the glass-basedarticles of Examples 8A and 8B was calculated in the same manner asExamples 4B-4D. The calculated stored tensile energy is plotted as afunction of measured CT (MPa), as shown in FIG. 31.

As shown in FIG. 31, Comparative 8A exhibited much greater storedtensile energy values for a given CT value than Example 8B (for the sameCT value). Specifically, at a CT of about 55 MPa, Comparative Example 8Aexhibited a stored tensile energy of about 8 J/m², whereas Example 8Bexhibited a stored tensile energy of about 3.5 J/m². Comparative Example8A and Example 8B were fractured and Example 8B fractured into fewerpieces than Comparative Example 8A, which fractured into a significantlygreater number of pieces. Accordingly, without being bound by theory, itis believed that controlling the stored tensile energy may provide a wayto control or predict fragmentation patterns or the number of fragmentsthat result from fracture.

Glass substrates having a nominal composition as shown in Table 2 andhaving a thicknesses of about 1 mm each were subjected to chemicalstrengthening in a molten salt bath including NaNO₃ and a temperature of430° C. for 4 hours (Comparative Example 8C) and for 61.5 hours (Example8D). Comparative Example 8C exhibited a known stress profile, whereas,Example 8D showed a stress profile according to one or more embodimentsof this disclosure. The stored tensile energy of Examples 8C and 8D wascalculated using the same method used with Examples 4B-4D and plotted asa function of measured CT (MPa), as shown in FIG. 32.

As shown in FIG. 32, Comparative 8C exhibited much greater storedtensile energy values for a given CT value than Example 8D (for the sameCT value). Comparative Example 8C and Example 8D were fractured andExample 8D fractured into fewer pieces than Comparative Example 8C,which fractured into a significantly greater number of pieces.

Example 9

Glass substrates having a nominal composition of 70.9 mol % SiO₂, 12.8mol % Al₂O₃, 1.95 mol % B₂O₃, 7.95 mol % Li₂O, 2.43 mol % Na₂O, 2.98 mol% MgO, 0.89 mol % ZnO, and 0.1 mol % SnO₂ and having a thicknesses ofabout 0.8 mm were subjected the ion exchange conditions of Table 5.Various properties of Example 9 are compared to Example 2 in Table 6.

TABLE 5 Ion exchange conditions for Example 9. Bath TemperatureCondition Bath Composition (° C.) Immersion time 1 100% NaNO₃ 430° C. 16hours 2 20% NaNO₃, 80% KNO3 430° C. 11 hours 3 100% NaNO₃ 430° C. 24hours 4 20% NaNO₃, 80% KNO₃ 430° C. 12.5 hours  

TABLE 6 Comparison of properties for Example 9B and Example 2. PropertyUnits Ex. 9B Ex. 2 Strain point ° C. 592 615 Anneal point ° C. 642 663Elastic Modulus GPa 81.4 83.8 Shear Modulus GPa 33.8 34.3 Poisson'sratio 0.211 0.222 CTE (RT-300° C.) ppm/° C. 4.58 3.84 ThermalConductivity W/cm*K SOC nm/cm/MPa 30.94 32.65 Refractive Index 1.50871.532 (at 550 nm)

The stress profiles of the glass-based articles of Example 9 weremeasured and exhibited the shapes described herein.

Glass substrates according to Example 2, Example 6, and ComparativeExample 9A were provided having the same thickness as Example 9. Theglass substrates according to Example 2 were ion exchanged in a moltenbath of 100% NaNO₃, having a temperature of 430° C. for 33 hours. Theglass substrates according to Example 6 were ion exchanged to exhibit aknown error function stress profile. Comparative Example 9A was ionexchanged in a molten bath of 100% NaNO₃, having a temperature of 390°C. for 16 hours and also exhibited a known error function stressprofile. As used herein, the term “error function stress profile” refersto a stress profile resembling FIG. 1.

The glass-based articles from Example 2, Comparative Example 6, Example9 and Comparative Example 9A were then retrofitted onto identical mobilephone devices. The phone devices were dropped from incremental heightsstarting at 20 centimeters onto 30 grit sandpaper. If a glass-basedarticle survived the drop from one height (e.g., 20 cm), the mobilephone was dropped again from a greater height (e.g., 30 cm, 40 cm, 50cm, etc.). The height at which the glass-based article failed is plottedin Example 32, which also shows the average failure height for thesamples of Examples 2, 6, and 9 and Comparative Example 9A. As shown inFIG. 33, Examples 2 and 9 exhibited failures at significantly greaterdrop height than Example 6 and Comparative Example 9A. Specifically,Examples 6 and Comparative Examples 9A exhibited failures at dropheights of about 38 cm and 55 cm, respectively, while Example 2 and 9exhibited failures at drop heights of about 147 cm and 132 cm,respectively.

The same test was repeated with new samples using the same mobile phonedevice onto 180 grit sandpaper. The average failure heights for Example6 was 190 cm, for Comparative Example 9A was 204 cm, for Example 2 was214 cm and for Example 9 was 214 cm.

Glass substrates according to Comparative Example 9B, having a nominalcomposition of 65 mol % SiO₂, 5 mol % B₂O₃, 14 mol % Al₂O₃, 14 mol %Na₂O, 2 mol % MgO, and 0.1 mol % SnO₂ and a thickness of 0.8 mm, wereion exchanged to exhibit a known error function stress profile Theglass-based article samples of Example 2 and Comparative Example 6(exhibiting the stress profile described above in this Example),Comparative Example 9B and the glass-based articles of Example 9 ionexchanged according to Condition 4, as shown in Table 5, were subjectedto A-ROR testing as described herein.

Examples 6 and 9 and Comparative Example 9B were abraded using a load orpressure of 25 psi and 45 psi, and Example 2 was abraded using a load of25 psi, only. The AROR data is shown in FIG. 34. As shown in FIG. 34,Examples 2 and 9 exhibited higher load to failure than Example 6, andComparative Example 9B.

Glass-based article samples of Examples 2 (ion exchanged as describedabove in this Example) and 9 (ion exchanged according to Condition 4)were subjected a 4-point bend test. The results are shown in the Weibulldistribution plot of FIG. 35. As shown in FIG. 35, Example 9 exhibitedhigher stress or load to failure (e.g., greater than about 400 MPa).

As shown above, glass-based articles made from compositions having astrain point greater than 525° C. enable ion exchange temperatures (orion exchange bath temperatures) in the range from about 350° C. to about480° C. In some embodiments, glass compositions exhibiting a diffusivitygreater than about 800 square micrometers/hour enable the metal oxidesdiffusing into the glass based article to penetrate the entire depth orthickness of the article quickly such that stress relaxation isminimized, Excessive stress relaxation can reduce the surfacecompressive stress of the glass-based article.

It will be apparent to those skilled in the art that variousmodifications and variations can be made without departing from thespirit or scope of the invention.

What is claimed is:
 1. A glass substrate comprising: from about 60 mol.% to about 70 mol. % SiO₂; from about 0 mol. % to about 5 mol. % MgO;from about 1 mol. % to about 2 mol. % CaO; and from about 2 mol. % toabout 10 mol. % Li₂O, wherein: a ratio of Li₂O to R₂O is greater than0.5 and less than or equal to 1, wherein R₂O is the sum (mol. %) ofLi₂O, K₂O, and Na₂O in the glass substrate; and the glass substrate issubstantially free of TiO₂; and the glass substrate is substantiallyfree of ZrO₂.
 2. The glass substrate of claim 1 further comprising fromabout 5 mol. % to about 28 mol. % Al₂O₃.
 3. The glass substrate of claim1, wherein Al₂O₃ is present in an amount from about 5 mol. % to about 20mol. %.
 4. The glass substrate of claim 1 further comprising from about0 mol. % to about 8 mol. % B₂O₃.
 5. The glass substrate of claim 1further comprising from about 0 mol. % to about 6 mol. % Na₂O.
 6. Theglass substrate of claim 1, wherein a difference between R₂O and Al₂O₃(R₂O—Al₂O₃) is from about −5 to about
 0. 7. The glass substrate of claim1, wherein a ratio of MgO to RO is from about 0 to about 1, wherein ROis the sum (mol. %) of BaO, CaO, MgO, PbO, SrO, and ZnO in the glasssubstrate.
 8. The glass substrate of claim 1 further comprising formabout 0 mol. % to about 2 mol. % SnO₂.
 9. An electronic devicecomprising the glass substrate of claim
 1. 10. A glass substratecomprising: from about 60 mol. % to about 70 mol. % SiO₂; from about 5mol. % to about 28 mol. % Al₂O₃; less than about 5 mol. % MgO; and fromabout 2 mol. % to about 10 mol. % Li₂O, wherein: a difference betweenR_(x)O and Al₂O₃ (R_(x)O—Al₂O₃)is from about 0 to about 3, whereinR_(x)O is the sum (mol. %) of BaO, CaO, MgO, PbO, SrO, ZnO, Li₂O, K₂O,and Na₂O in the glass substrate; and the glass substrate issubstantially free of TiO₂.
 11. The glass substrate of claim 10 furthercomprising from about 5 mol. % to about 20 mol. % Al₂O₃.
 12. The glasssubstrate of claim 10 further comprising from about 0.1mol. % to about 4mol. % B₂O₃.
 13. The glass substrate of claim 10, wherein the glasssubstrate is substantially free of B₂O₃.
 14. The glass substrate ofclaim 10 further comprising from about 0 mol. % to about 6 mol. % Na₂O.15. The glass substrate of claim 10 further comprising from about 0mol.% to about 2 mol. % ZnO.
 16. The glass substrate of claim 10, whereinthe glass substrate is substantially free of ZrO₂.
 17. The glasssubstrate of claim 10, wherein a ratio of MgO to RO is from about 0 toabout 1, wherein RO is the sum (mol.%) of BaO, CaO, MgO, PbO, SrO, andZnO in the glass substrate.
 18. The glass substrate of claim 10 furthercomprising form about 0mol. % to about 2 mol. % SnO₂.
 19. The glasssubstrate of claim 10 further comprising from about 0.1mol. % to about10 mol. % P₂O₅.
 20. An electronic device comprising the glass substrateof claim 10.